pith. machine review for the scientific record. sign in

arxiv: 2603.24667 · v2 · submitted 2026-03-25 · ✦ hep-th

Recognition: unknown

The Art of Branching: Cobordism Junctions of 10d String Theories

Chiara Altavista , Edoardo Anastasi , Roberta Angius , Angel M. Uranga
Authors on Pith no claims yet

Pith reviewed 2026-05-15 00:08 UTC · model grok-4.3

classification ✦ hep-th
keywords cobordism junctions10d string theoriesworldsheet interpolationsRG flowtype 0B descendantsorientifoldsheterotic stringssupercritical dimensions
0
0 comments X

The pith

10d string theories join at 9d junctions via worldsheet RG interpolations

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs explicit configurations in which several 10-dimensional string theories join at a 9-dimensional junction. This provides a dynamical microscopic realization of cobordisms between different string theories using generalized renormalization group flow interpolations on the worldsheet. Extra degrees of freedom in the construction remain gapped away from the junction but become critical at the branch point, enabling the transition between theories. One explicit example assembles a four-branch junction connecting type IIB with type I, the non-supersymmetric USp(32) theory, and the U(32) orientifold of type 0B theory.

Core claim

Configurations of several 10d string theories join at a 9d junction, providing a dynamical realization of cobordisms between multiple 10d string theories. The interpolations involve additional degrees of freedom that are gapped except at the branch point, where the gap closes to trigger the branching transition. The extra degrees of freedom admit an interpretation as additional dimensions in a supercritical string theory that reduces to the 10d junction configuration upon closed tachyon condensation, although quantum corrections turn the core into a strongly coupled lightlike region.

What carries the argument

Generalized worldsheet RG flow interpolations in which extra degrees of freedom gap except at the branch point, where the gap closes to connect different 10d string theories.

Load-bearing premise

The extra degrees of freedom can be interpreted as additional dimensions in a supercritical string theory whose closed tachyon condensation produces the described 10d junction configuration.

What would settle it

A direct worldsheet calculation at the junction point that reveals an inconsistency between the proposed gapped extra modes and the expected spectrum or beta functions of the connected 10d theories.

read the original abstract

We describe the explicit construction of configurations of several 10d string theories joining at a 9d junction, providing a dynamical realization of cobordisms between multiple 10d string theories, predicted by the Cobordism Conjecture. We provide the microscopic worldsheet description of the configuration in a generalization of the `going up and down the RG flow' interpolations recently used in the description of IIA/IIB domain wall. The interpolations involve additional degrees of freedom, which are gapped except at the branch point, at which the gap closes and triggers the branching transition. The extra degrees of freedom admit an interpretation in terms of additional dimensions in a supercritical string theory, which reduces to the 10d junction configuration upon closed tachyon condensation. Quantum corrections of the 2d worldsheet theory turn the junction into a strongly coupled lightlike core whose UV resolution lies beyond worldsheet techniques. We construct explicit examples of junctions of 10d heterotic string theories, type 0, and type II theories and orientifolds thereof. Our explicit examples include junctions of 10d chiral theories whose chiral fields flow between different branches. One particularly nice configuration is a 4-branch junction of the IIB theory, with type I, the non-supersymmetric $USp(32)$ theory and the $U(32)$ orientifold of 0B theory, thus assembling the four non-tachyonic descendants of type 0B theory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper claims to construct explicit configurations of multiple 10d string theories joining at 9d junctions, realizing cobordisms predicted by the Cobordism Conjecture via a microscopic worldsheet description. This generalizes recent RG-flow interpolations for domain walls by introducing additional gapped degrees of freedom that become massless at the branch point, interpreted as extra dimensions from a supercritical string theory that reduces to the 10d junction upon closed tachyon condensation. Examples include junctions of heterotic, type 0, and type II theories and orientifolds, with a highlighted 4-branch junction assembling IIB, type I, the non-supersymmetric USp(32) theory, and the U(32) orientifold of 0B theory. The construction notes that quantum corrections turn the junction into a strongly coupled lightlike core whose UV resolution lies beyond worldsheet techniques.

Significance. If the central constructions are made fully consistent, the work would supply concrete dynamical realizations of multi-branch cobordism junctions in 10d string theory, extending domain-wall interpolations to chiral field flows between branches and assembling the four non-tachyonic 0B descendants. This strengthens the Cobordism Conjecture with explicit worldsheet models grounded in RG flows and tachyon condensation, offering a useful advance for understanding string vacua connections.

major comments (2)
  1. [Abstract] The statement that the UV resolution of the strongly coupled lightlike core lies beyond worldsheet techniques (Abstract) is load-bearing for the dynamical consistency claim; without an explicit reduction or consistency check for the extra gapped degrees of freedom at the branch point, the microscopic realization of the junctions remains formally incomplete.
  2. [the construction of the 4-branch junction] The interpretation of the extra degrees of freedom as arising from additional dimensions in a supercritical string theory that reduces to the 10d junction upon closed tachyon condensation requires further justification, as the gap closing at the 9d branch point introduces a strongly coupled regime whose consistency is not demonstrated within the presented methods.
minor comments (1)
  1. [the discussion of the interpolations] Clarify the precise mechanism by which the gapped degrees of freedom become massless exactly at the branch point to improve the readability of the RG-flow interpolation description.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address each major comment point by point below, providing clarifications and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] The statement that the UV resolution of the strongly coupled lightlike core lies beyond worldsheet techniques (Abstract) is load-bearing for the dynamical consistency claim; without an explicit reduction or consistency check for the extra gapped degrees of freedom at the branch point, the microscopic realization of the junctions remains formally incomplete.

    Authors: We agree that the abstract statement is central and that the strong-coupling regime at the branch point limits what can be demonstrated within worldsheet methods. Our construction provides an explicit worldsheet CFT description of the RG-flow interpolation with gapped modes that close at the junction, with consistency argued via the standard closed tachyon condensation mechanism and the fact that the theories reduce to well-defined 10d string theories away from the core. We do not claim a complete UV resolution beyond this framework, as explicitly noted. To address the concern, we will revise the abstract for precision and expand the main text with additional discussion of the effective description, regime of validity, and consistency checks from the RG flow perspective. revision: partial

  2. Referee: [the construction of the 4-branch junction] The interpretation of the extra degrees of freedom as arising from additional dimensions in a supercritical string theory that reduces to the 10d junction upon closed tachyon condensation requires further justification, as the gap closing at the 9d branch point introduces a strongly coupled regime whose consistency is not demonstrated within the presented methods.

    Authors: The interpretation follows from the established role of closed tachyon condensation in supercritical string theories, where extra dimensions are effectively reduced. We provide explicit worldsheet constructions for the 4-branch junction (IIB, type I, USp(32), and U(32) 0B orientifold) using generalized RG interpolations. The gap closing is part of the branching transition, with the strongly coupled core acknowledged as outside perturbative worldsheet control. We will add further justification by elaborating on the tachyon condensation literature parallels and detailing how the gapped modes are integrated out in the effective 9d theory, including a revised subsection on the 4-branch example. revision: partial

standing simulated objections not resolved
  • Explicit UV resolution or non-perturbative consistency check of the strongly coupled lightlike core at the junction, which lies beyond worldsheet techniques as stated in the manuscript.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper constructs explicit 10d string theory junctions by generalizing prior RG-flow interpolations for domain walls, using worldsheet descriptions and supercritical string interpretations for extra degrees of freedom. The central claims rely on standard string theory tools and stated assumptions about tachyon condensation whose consistency is explicitly noted as lying beyond worldsheet control, without any reduction of predictions to fitted parameters, self-definitions, or load-bearing self-citations that are unverified. No equations or steps equate outputs to inputs by construction, and the assembly of known non-tachyonic 0B descendants follows from the explicit branching configurations rather than renaming or imported uniqueness theorems.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 2 invented entities

The paper relies on established string theory axioms and introduces new configurations and interpretations without new fundamental particles or forces.

axioms (3)
  • domain assumption The Cobordism Conjecture holds for 10d string theories
    The paper provides dynamical realizations of its predictions.
  • domain assumption Worldsheet CFT and RG flow interpolations are applicable to these junction configurations
    Used as the microscopic description.
  • domain assumption Closed tachyon condensation reduces the supercritical theory to the 10d junction
    Central to the interpretation of extra degrees of freedom.
invented entities (2)
  • 9d junction configuration with branch point no independent evidence
    purpose: To realize the cobordism between multiple 10d theories
    New setup introduced for the dynamical realization.
  • Extra gapped degrees of freedom at the branch point no independent evidence
    purpose: To trigger the branching transition when gap closes
    Additional DOF in the worldsheet theory.

pith-pipeline@v0.9.0 · 5571 in / 1715 out tokens · 67767 ms · 2026-05-15T00:08:42.078056+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Sharpened Dynamical Cobordism

    hep-th 2026-05 unverdicted novelty 7.0

    Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.

  2. Ho\v{r}ava-Witten theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ as type 0 orientifold

    hep-th 2026-03 unverdicted novelty 7.0

    Hořava-Witten theory on S¹∨S¹ is dual to a type 0B orientifold with SO(16)^4 gauge group, explaining gauge group doubling via the geometry's junction and revealing two variants from E8 wall orientations.

  3. A Duality Web for Non-Supersymmetric Strings

    hep-th 2026-04 unverdicted novelty 6.0

    A duality web is proposed in which Z2 quotients of M-theory on S1 vee S1 and F-theory on (S1 vee S1) x S1 map to 0A/0B orientifolds and non-supersymmetric E-type and D-type heterotic strings, providing evidence for ex...

  4. Heterotic Ouroboros

    hep-th 2026-04 unverdicted novelty 5.0

    M-theory on S1 vee S1 with quotients and type I' mechanisms reproduces the light spectra and gauge groups of 10D heterotic theories, with evidence for junctions among them.

  5. Heterotic Ouroboros

    hep-th 2026-04 unverdicted novelty 5.0

    A consistent set of rules from M-theory on S¹ ∨ S¹ combined with type I' enhancements reproduces the light spectra, gauge groups, and global structure of ten-dimensional heterotic string theories, with indications of ...

Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages · cited by 4 Pith papers · 26 internal anchors

  1. [1]

    The String Landscape and the Swampland

    C. Vafa,The String landscape and the swampland,hep-th/0509212

    work page internal anchor Pith review Pith/arXiv arXiv

  2. [2]

    McNamara and C

    J. McNamara and C. Vafa,Cobordism Classes and the Swampland,arXiv:1909.10355

    work page arXiv 1909

  3. [3]

    Heterotic and Type I String Dynamics from Eleven Dimensions

    P. Horava and E. Witten,Heterotic and type I string dynamics from eleven-dimensions,Nucl. Phys. B460(1996) 506–524, [hep-th/9510209]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  4. [4]

    Eleven-Dimensional Supergravity on a Manifold with Boundary

    P. Horava and E. Witten,Eleven-dimensional supergravity on a manifold with boundary,Nucl. Phys. B475(1996) 94–114, [hep-th/9603142]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  5. [5]

    M-theory boundaries beyond supersymmetry,

    M. Montero and L. Zapata,M-theory boundaries beyond supersymmetry,JHEP07 (2025) 090, [arXiv:2504.06985]. – 59 –

    work page arXiv 2025

  6. [6]

    Evidence for Heterotic - Type I String Duality

    J. Polchinski and E. Witten,Evidence for heterotic - type I string duality,Nucl. Phys. B460(1996) 525–540, [hep-th/9510169]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  7. [7]

    Buratti, M

    G. Buratti, M. Delgado, and A. M. Uranga,Dynamical tadpoles, stringy cobordism, and the SM from spontaneous compactification,JHEP06(2021) 170, [arXiv:2104.02091]

    work page arXiv 2021

  8. [8]

    Buratti, J

    G. Buratti, J. Calder´ on-Infante, M. Delgado, and A. M. Uranga,Dynamical Cobordism and Swampland Distance Conjectures,JHEP10(2021) 037, [arXiv:2107.09098]

    work page arXiv 2021

  9. [9]

    Angius, J

    R. Angius, J. Calder´ on-Infante, M. Delgado, J. Huertas, and A. M. Uranga,At the end of the world: Local Dynamical Cobordism,JHEP06(2022) 142, [arXiv:2203.11240]

    work page arXiv 2022

  10. [10]

    Blumenhagen, N

    R. Blumenhagen, N. Cribiori, C. Kneissl, and A. Makridou,Dynamical Cobordism of a Domain Wall and its Companion Defect 7-brane,arXiv:2205.09782

    work page arXiv

  11. [11]

    Angius, M

    R. Angius, M. Delgado, and A. M. Uranga,Dynamical Cobordism and the beginning of time: supercritical strings and tachyon condensation,JHEP08(2022) 285, [arXiv:2207.13108]

    work page arXiv 2022

  12. [12]

    Angius, J

    R. Angius, J. Huertas, and A. M. Uranga,Small black hole explosions,JHEP06 (2023) 070, [arXiv:2303.15903]

    work page arXiv 2023

  13. [13]

    Blumenhagen, C

    R. Blumenhagen, C. Kneissl, and C. Wang,Dynamical Cobordism Conjecture: Solutions for End-of-the-World Branes,arXiv:2303.03423

    work page arXiv

  14. [14]

    Angius, A

    R. Angius, A. Makridou, and A. M. Uranga,Intersecting end of the world branes, JHEP03(2024) 110, [arXiv:2312.16286]

    work page arXiv 2024

  15. [15]

    Angius,End of The World brane networks for infinite distance limits in CY moduli space, 2404.14486

    R. Angius,End of The World brane networks for infinite distance limits in CY moduli space,arXiv:2404.14486

    work page arXiv

  16. [16]

    Delgado,The bubble of nothing under T-duality,JHEP05(2024) 333, [arXiv:2312.09291]

    M. Delgado,The bubble of nothing under T-duality,JHEP05(2024) 333, [arXiv:2312.09291]

    work page arXiv 2024

  17. [17]

    Antonelli and I

    R. Antonelli and I. Basile,Brane annihilation in non-supersymmetric strings,Journal of High Energy Physics2019(Nov., 2019)

    work page 2019

  18. [18]

    J. J. Heckman, J. McNamara, J. Parra-Martinez, and E. Torres,GSO Defects: IIA/IIB Walls and the Surprisingly StableR7-Brane,arXiv:2507.21210

    work page arXiv

  19. [19]

    Anastasi, M

    E. Anastasi, M. Montero, A. M. Uranga, and C. Wang,What IIB looks IIA string: String Cobordisms via Non-Compact CFTs,arXiv:2603.00225

    work page arXiv

  20. [20]

    Torres,A Matrix Theory Construction of the IIA/IIB Wall,arXiv:2603.02199

    E. Torres,A Matrix Theory Construction of the IIA/IIB Wall,arXiv:2603.02199. – 60 –

    work page arXiv

  21. [21]

    Dynamical Cobordisms in General Relativity and String Theory

    S. Hellerman and M. Kleban,Dynamical Cobordisms in General Relativity and String Theory,JHEP02(2011) 022, [arXiv:1009.3277]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  22. [22]

    A Note On Some Minimally Supersymmetric Models In Two Dimensions

    D. Gaiotto, T. Johnson-Freyd, and E. Witten, “A note on some minimally supersymmetric models in two dimensions..” arxiv preprint 1902.10249, 2021

    work page internal anchor Pith review Pith/arXiv arXiv 1902

  23. [23]

    Witten,Elliptic Genera and Quantum Field Theory,Commun

    E. Witten,Elliptic Genera and Quantum Field Theory,Commun. Math. Phys.109 (1987) 525

    work page 1987

  24. [24]

    4-manifolds and topological modular forms

    S. Gukov, D. Pei, P. Putrov, and C. Vafa,4-manifolds and topological modular forms, JHEP05(2021) 084, [arXiv:1811.07884]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  25. [25]

    Tachikawa,Topological modular forms and the absence of a heterotic global anomaly,PTEP2022(2022), no

    Y. Tachikawa,Topological modular forms and the absence of a heterotic global anomaly,PTEP2022(2022), no. 4 04A107, [arXiv:2103.12211]

    work page arXiv 2022

  26. [26]

    Tachikawa and M

    Y. Tachikawa and M. Yamashita,Topological Modular Forms and the Absence of All Heterotic Global Anomalies,Commun. Math. Phys.402(2023), no. 2 1585–1620, [arXiv:2108.13542]. [Erratum: Commun.Math.Phys. 402, 2131 (2023)]

    work page arXiv 2023

  27. [27]

    Tachikawa, M

    Y. Tachikawa, M. Yamashita, and K. Yonekura,Remarks on Mod-2 Elliptic Genus, Commun. Math. Phys.406(2025), no. 1 16, [arXiv:2302.07548]

    work page arXiv 2025

  28. [28]

    Tachikawa,On a long exact sequence of groups of equivalence classes of 2dN=(0,1) SQFTs,arXiv:2509.12481

    Y. Tachikawa,On a long exact sequence of groups of equivalence classes of 2dN=(0,1) SQFTs,arXiv:2509.12481

    work page arXiv

  29. [29]

    G. W. Moore, V. Saxena, and w. a. a. b. D. S. Freed,TASI Lectures On Topological Field Theories And Differential Cohomology, inTheoretical Advanced Study Institute in Elementary Particle Physics 2023: Aspects of Symmetry, 10, 2025.arXiv:2510.07408

    work page arXiv 2023

  30. [30]

    Bautista, A

    T. Bautista, A. Dabholkar, and H. Erbin,Quantum Gravity from Timelike Liouville theory,JHEP10(2019) 284, [arXiv:1905.12689]

    work page arXiv 2019

  31. [31]

    Cosmological solutions of supercritical string theory

    S. Hellerman and I. Swanson,Cosmological solutions of supercritical string theory, Phys. Rev. D77(2008) 126011, [hep-th/0611317]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  32. [32]

    Cosmological unification of string theories

    S. Hellerman and I. Swanson,Cosmological unification of string theories,JHEP07 (2008) 022, [hep-th/0612116]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  33. [33]

    Dimension-changing exact solutions of string theory

    S. Hellerman and I. Swanson,Dimension-changing exact solutions of string theory, JHEP09(2007) 096, [hep-th/0612051]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  34. [34]

    Charting the landscape of supercritical string theory

    S. Hellerman and I. Swanson,Charting the landscape of supercritical string theory, Phys. Rev. Lett.99(2007) 171601, [arXiv:0705.0980]. – 61 –

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  35. [35]

    Supercritical N = 2 string theory

    S. Hellerman and I. Swanson,Supercritical N = 2 string theory,arXiv:0709.2166

    work page internal anchor Pith review Pith/arXiv arXiv

  36. [36]

    A stable vacuum of the tachyonic E8 string

    S. Hellerman and I. Swanson,A Stable vacuum of the tachyonic E(8) string, arXiv:0710.1628

    work page internal anchor Pith review Pith/arXiv arXiv

  37. [37]

    Light-like tachyon condensation in Open String Field Theory

    S. Hellerman and M. Schnabl,Light-like tachyon condensation in Open String Field Theory,JHEP04(2013) 005, [arXiv:0803.1184]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  38. [38]

    Discrete gauge symmetries from (closed string) tachyon condensation

    M. Berasaluce-Gonz’alez, M. Montero, A. Retolaza, and A. M. Uranga,Discrete gauge symmetries from (closed string) tachyon condensation,JHEP11(2013) 144, [arXiv:1305.6788]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  39. [39]

    I. n. Garc´ ıa-Etxebarria, M. Montero, and A. Uranga,Heterotic NS5-branes from closed string tachyon condensation,Phys. Rev. D90(2014), no. 12 126002, [arXiv:1405.0009]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  40. [40]

    Closed tachyon solitons in type II string theory

    I. Garc´ ıa-Etxebarria, M. Montero, and A. M. Uranga,Closed tachyon solitons in type II string theory,Fortsch. Phys.63(2015) 571–595, [arXiv:1505.05510]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  41. [41]

    Angius, A

    R. Angius, A. M. Uranga, and C. Wang,End of the world boundaries for chiral quantum gravity theories,JHEP03(2025) 064, [arXiv:2410.07322]

    work page arXiv 2025

  42. [42]

    S. S. Razamat and D. Tong,Gapped Chiral Fermions,arXiv:2009.05037

    work page arXiv 2009

  43. [43]

    Tong,Comments on symmetric mass generation in 2d and 4d,JHEP07(2022) 001 [2104.03997]

    D. Tong,Comments on symmetric mass generation in 2d and 4d,JHEP07(2022) 001, [arXiv:2104.03997]

    work page arXiv 2022

  44. [44]

    Wang and Y.-Z

    J. Wang and Y.-Z. You,Symmetric Mass Generation,Symmetry14(2022), no. 7 1475, [arXiv:2204.14271]

    work page arXiv 2022

  45. [45]

    Anomaly Cancellations in the Type I D9-anti-D9 System and the USp(32) String Theory

    S. Sugimoto,Anomaly cancellations in type I D-9 - anti-D-9 system and the USp(32) string theory,Prog. Theor. Phys.102(1999) 685–699, [hep-th/9905159]

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  46. [46]

    Some Properties of Open - String Theories

    A. Sagnotti,Some properties of open string theories, inInternational Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY 95), pp. 473–484, 9, 1995.hep-th/9509080

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  47. [47]

    Surprises in Open-String Perturbation Theory

    A. Sagnotti,Surprises in open string perturbation theory,Nucl. Phys. B Proc. Suppl. 56(1997) 332–343, [hep-th/9702093]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  48. [48]

    D-branes in non-tachyonic 0B orientifolds

    E. Dudas and J. Mourad,D-branes in nontachyonic 0B orientifolds,Nucl. Phys. B598 (2001) 189–224, [hep-th/0010179]. – 62 –

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  49. [49]

    Open Strings

    C. Angelantonj and A. Sagnotti,Open strings,Phys. Rept.371(2002) 1–150, [hep-th/0204089]. [Erratum: Phys.Rept. 376, 407 (2003)]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  50. [50]

    Raucci,Spacetime aspects of non-supersymmetric strings

    S. Raucci,Spacetime aspects of non-supersymmetric strings. PhD thesis, Scuola Normale Superiore, Italy, Pisa, Scuola Normale Superiore, Pisa, Scuola Normale Superiore, 9, 2024.arXiv:2409.19395

    work page arXiv 2024

  51. [51]

    Z. K. Baykara, E. Dudas, and C. Vafa,M-theory onS 1 ∨S 1 as Type 0A, arXiv:2603.13468

    work page arXiv

  52. [52]

    Ho\v{r}ava-Witten theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ as type 0 orientifold

    C. Altavista, E. Anastasi, S. Raucci, A. M. Uranga, and C. Wang,Hoˇ rava-Witten theory onS 1 ∨S 1 as type 0 orientifold,arXiv:2603.25786

    work page internal anchor Pith review Pith/arXiv arXiv

  53. [53]

    Tachikawa,On the trivalent junction of three non-tachyonic heterotic string theories,arXiv:2603.28133

    Y. Tachikawa,On the trivalent junction of three non-tachyonic heterotic string theories,arXiv:2603.28133

    work page arXiv

  54. [54]

    Basile, A

    I. Basile, A. Debray, M. Delgado, and M. Montero,Global anomalies & bordism of non-supersymmetric strings,JHEP02(2024) 092, [arXiv:2310.06895]

    work page arXiv 2024

  55. [55]

    Tachikawa and H

    Y. Tachikawa and H. Y. Zhang,On aZ 3-valued discrete topological term in 10d heterotic string theories,SciPost Phys.17(2024), no. 3 077, [arXiv:2403.08861]

    work page arXiv 2024

  56. [56]

    Polchinski,String theory

    J. Polchinski,String theory. Vol. 2: Superstring theory and beyond. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 12, 2007

    work page 2007

  57. [57]

    L. J. Dixon and J. A. Harvey,String Theories in Ten-Dimensions Without Space-Time Supersymmetry,Nucl. Phys. B274(1986) 93–105

    work page 1986

  58. [58]

    Seiberg and E

    N. Seiberg and E. Witten,Spin Structures in String Theory,Nucl. Phys. B276(1986) 272

    work page 1986

  59. [59]

    Alvarez-Gaume, P

    L. Alvarez-Gaume, P. H. Ginsparg, G. W. Moore, and C. Vafa,An O(16) x O(16) Heterotic String,Phys. Lett. B171(1986) 155–162

    work page 1986

  60. [60]

    Kawai, D

    H. Kawai, D. C. Lewellen, and S. H. H. Tye,Classification of Closed Fermionic String Models,Phys. Rev. D34(1986) 3794

    work page 1986

  61. [61]

    Dynamical Dimension Change in Supercritical String Theory

    S. Hellerman and X. Liu,Dynamical dimension change in supercritical string theory, hep-th/0409071

    work page internal anchor Pith review Pith/arXiv arXiv

  62. [62]

    On the Landscape of Superstring Theory in D > 10

    S. Hellerman,On the landscape of superstring theory in D>10,hep-th/0405041

    work page internal anchor Pith review Pith/arXiv arXiv

  63. [63]

    Observations On The Moduli Space Of Two Dimensional String Theory

    N. Seiberg,Observations on the moduli space of two dimensional string theory,JHEP 03(2005) 010, [hep-th/0502156]. – 63 –

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  64. [64]

    Boyle Smith and Y

    P. Boyle Smith and Y. Zheng,Backfiring Bosonisation,arXiv:2403.03953. – 64 –

    work page arXiv