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A Pathway to Decay and Fission of Orthosymplectic Quiver Theories

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Pith's one-line read An algorithm—Orthosymplectic Decay and Fission—derives the full Coulomb branch Hasse diagram of any simply-laced orthosymplectic 3d N=4 quiver, predicting every descendant theory from Coulomb branch Higgsing.

desk verdict Real extension of Decay and Fission to orthosymplectic quivers with genuine new predictions, but the goodness criterion is calibrated only for USp(2) neighbours of SO(6) and the b=-1 vacuum analysis is missing, so 'all descendants' is not yet established. read the letter →

arxiv 2412.15202 v1 pith:TR6AKRQT submitted 2024-12-19 hep-th

Craig Lawrie , Lorenzo Mansi , Marcus Sperling , Zhenghao Zhong This is my paper · ORCID
classification hep-th
keywords orthosymplecticquiversDecayandFissionCoulombbranchHassediagramsymplecticsingularityHiggsRGflowmagneticquiverclassStheories
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes an algorithm that takes any 3d $\mathcal{N}=4$ quiver gauge theory built from orthogonal and symplectic gauge nodes and returns the full Hasse diagram of its Coulomb branch: the ordered collection of singular strata, each connected to the next by a transverse slice, which is the moduli space of the residual theory after Higgsing. Physically, each stratum is a distinct way of giving vacuum expectation values to monopole operators, so the diagram is a complete account of Coulomb branch Higgsing. The rules are validated through the Lie algebra isomorphism $\mathfrak{su}(4)\cong\mathfrak{so}(6)$, where the same moduli space admits both a unitary and an orthosymplectic quiver description, allowing direct comparison with the established unitary Decay and Fission algorithm. The paper then uses the algorithm to predict new Higgs branch renormalization group flows of 6d $\mathcal{N}=(1,0)$ D-type orbi-instanton theories and of class $\mathcal{S}$ theories of type $\mathfrak{so}(2N)$, including flows that split a theory into a product of interacting fixed points. A stated conjecture—that quiver theories with identical Coulomb branch Hasse diagrams are different presentations of the same theory—is what lets the algorithm remove redundant descendant quivers and produce a genuine Hasse diagram.

What carries the argument

The load-bearing object is the Orthosymplectic Decay and Fission algorithm of Section 2. It starts from a per-node balance, the local measure of whether monopole operators stay above the unitarity bound, together with a modified balance rule for $\mathrm{SO}(6)$ nodes: a neighbouring $\mathrm{Usp}(2)$ node counts as $5/8$ of a flavour, or $5/4$ when it sits between an $\mathrm{SO}(6)$ and an $\mathrm{SO}(2)$ node. This modification makes the goodness test sensitive to monopole operators valued in the half-integer charge lattice, which the ordinary balance misses. The algorithm then applies two operations: decay, which subtracts the maximal allowed labels from balanced nodes according to a table of transverse slices ($d_n$, $b_n$, $a_7$, $a_5$, $a_4$, $a_2$, $a_1$, $e_7$, $e_8$), and fission, which uses the Levi decompositions $\mathfrak{so}(2N)\to\mathfrak{so}(2N-2K)\oplus\mathfrak{u}(K)$ and $\mathfrak{usp}(2N)\to\mathfrak{usp}(2N-2K)\oplus\mathfrak{u}(K)$ to split the quiver into an orthosymplectic factor and a unitary factor; unitarisation is the case $K=N$, where only the unitary factor remains. The unitary factor is then processed further by the standard unitary Decay and Fission rules.

What would settle it

Compute an independent invariant—the Coulomb branch Hilbert series where the quiver is good, or the Hall–Littlewood index or the class $\mathcal{S}$ spectrum where it is not—for two quivers that the algorithm identifies as equivalent, such as the pair in equation (3.12); if the invariants differ, the identification conjecture fails. A single orthosymplectic quiver whose algorithmically predicted Hasse diagram disagrees with the diagram of its independently known unitary dual, for any of the $\mathfrak{so}(2N)$ class $\mathcal{S}$ flows checked against the existing D-type classification, would similarly falsify the rules.

Watch

Extended reading notes

Core claim

The central claim is that Coulomb branch Higgsing of simply-laced orthosymplectic quivers is governed by two elementary moves, decay and fission, with unitarisation as the limiting case of fission. Decay lowers the ranks of balanced gauge nodes according to a small table of allowed transverse slices; fission splits an $\mathfrak{so}(2N)$ node into $\mathfrak{so}(2N-2K)\oplus\mathfrak{u}(K)$ or a $\mathfrak{usp}(2N)$ node into $\mathfrak{usp}(2N-2K)\oplus\mathfrak{u}(K)$, producing a product of an orthosymplectic quiver and a unitary quiver, and unitarisation is the case where the orthosymplectic factor disappears entirely. Through the $\mathfrak{su}(4)\cong\mathfrak{so}(6)$ class $\mathcal{S}$ mirror pairs, the paper shows that these rules reproduce the full Coulomb branch Hasse diagrams already known from unitary Decay and Fission, including all cases with enhanced flavour symmetry. Beyond that benchmark, the algorithm predicts that the magnetic quiver of the rank-$N$ D-type orbi-instanton fissions, for each $0<\ell\leq N$, into the rank-$(N-\ell)$ orbi-instanton quiver times the rank-$\ell$ E-string quiver (the 6d theory of M5-branes without an orbifold), matching the picture of separating stacks of M5-branes, and that class $\mathcal{S}$ theories of type $\mathfrak{so}(12)$ flow through the Levi splitting $\mathfrak{so}(12)\to\mathfrak{so}(8)\oplus\mathfrak{su}(2)$ into a product of class $\mathcal{S}$ theories of type $\mathfrak{so}(8)$ and $\mathfrak{su}(2)$.

Load-bearing premise

The algorithm does not itself decide which of the descendant quivers it produces are redundant; it relies on the paper's conjecture that two quiver theories with identical Coulomb branch diagrams are different presentations of the same theory, and without that identification the tentative diagram cannot be reduced to a unique final answer.

Editorial extensions

If this is right

  • For any simply-laced orthosymplectic quiver with edge multiplicity one, the Coulomb branch stratification—all symplectic leaves and their transverse slices—becomes algorithmically accessible, not only for star-shaped or class $\mathcal{S}$ examples.
  • Class $\mathcal{S}$ theories of type $\mathfrak{so}(2n)$ obtain a complete Higgs branch Hasse diagram from their 3d mirror, including Higgsings beyond partial puncture closure that were previously inaccessible from the mirror perspective.
  • The D-type orbi-instanton magnetic quiver fissions, for each $0<\ell\leq N$, into the product of the rank-$(N-\ell)$ orbi-instanton quiver and the rank-$\ell$ E-string quiver, realising the expected separation of M5-branes; the paper states this is the first explicit demonstration beyond the $\mathfrak{su}(K)$ case.
  • The algorithm predicts new class $\mathcal{S}$ Higgs branch RG flows from Levi decompositions, such as $\mathfrak{so}(12)\to\mathfrak{so}(8)\oplus\mathfrak{su}(2)$, including two distinct flow paths between $S_{\mathfrak{so}(12)}$ and $S_{\mathfrak{so}(6)}$, which supports the simultaneous-deletion proposal for higher-rank class $\mathcal{S}$.
  • Orthosymplectic quivers can fission into mixed products with unitary quivers or unitarise entirely to a unitary quiver, after which the standard unitary Decay and Fission algorithm takes over; redundant equivalent quivers are identified by the paper's identical-Hasse-diagram conjecture.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the identical-Hasse-diagram conjecture is correct, the same criterion could serve as a practical equivalence test for symplectic singularities, deciding when two different-looking 3d $\mathcal{N}=4$ quivers describe the same space even when a Hilbert series comparison is unavailable.
  • The fractional-balance prescription for $\mathrm{SO}(6)$ suggests that half-integer lattice monopole effects might be localisable as fractional flavour contributions more generally; testing whether an analogous readjustment exists for other $\mathrm{SO}(2K)$ nodes would sharpen or generalise Rule 1.
  • Applying the algorithm to the additional unitary/orthosymplectic dual pairs catalogued in the quotient-quiver-subtraction literature would provide further independent checks, as the paper itself suggests.
  • Because the 6d flows are mirrored by complex-structure deformations in F-theory, the algorithm could be run in reverse: given a predicted Hasse diagram, one could search for the corresponding Calabi–Yau deformation or tensor-branch curve configuration that engineers the same Higgsing pattern.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes an algorithm, termed Orthosymplectic Decay and Fission, for computing Coulomb branch Hasse diagrams of 3d N=4 orthosymplectic quiver gauge theories. The algorithm extends the known unitary Decay and Fission procedure: Rule 1 modifies the balance of SO(6) nodes by assigning effective fractional flavour contributions to neighbouring USp(2) nodes (5/8 or 5/4); Rules 2 and 3 specify when decays are admissible and which decays are allowed; Rules 4a and 4b introduce fission and unitarisation into products with unitary quivers. The authors validate the algorithm on su(4) ~ so(6) class S theories, where orthosymplectic mirrors can be compared with unitary mirrors, and then apply it to 6d D-type orbi-instanton theories and higher-rank so(2N) class S theories, obtaining new predictions for Higgs branch RG flows. The paper contains a detailed worked example, an extended class S comparison, and an appendix application to T^sigma_rho(SO(16)).

Significance. If the proposed algorithm is correct, it is a significant technical advance: it extends a powerful method for extracting symplectic stratifications from unitary quivers to orthosymplectic quivers, with immediate applications to the Higgs branches of higher-dimensional SCFTs. The paper's concrete strengths are its systematic treatment of the su(4)-type class S examples with enhanced flavour symmetry, the cross-checks using Hilbert series and known geometries (for instance the d4 x d4 identification in eq. (2.9)), and the D-type orbi-instanton fission prediction in eqs. (5.9) and (5.10), which goes beyond previously studied g = su(K) cases. The presentation is generally clear and the examples are worked in detail. However, the central admissibility criterion is calibrated rather than derived, and the announced scope -- 'all descendant theories' for all simply-laced orthosymplectic quivers with edge multiplicity one -- is not yet established by the evidence presented.

major comments (4)
  1. [§4.1 and eq. (3.20), Rule 1] The effective fractional flavour contributions in Rule 1 are fitted to the su(4) ~ so(6) class S examples in (4.1), and the only half-integer-lattice monopole computation given is for an SO(2K) node with n USp(2) neighbours, eq. (3.20). The paper then applies the algorithm to quivers containing SO(6) nodes adjacent to USp(4) or larger symplectic nodes, e.g. the D-type orbi-instanton magnetic quiver (5.8) and the class S quiver (5.17). In this regime the calibrated 5/8 and 5/4 contributions have no demonstrated validity, so the admissibility of the generated quivers -- and hence the claimed Hasse diagrams -- is not established by the manuscript. A concrete way to close this gap would be to generalise the monopole R-charge computation of eq. (3.20) to USp(2r) neighbours and to test whether Rule 1 reproduces those thresholds.
  2. [§4.2, Rules 2 and 3b] Rule 2 and Rule 3b admit gauge nodes with balance b = -1 of any orthosymplectic kind, but §4.2 explicitly states that an analysis for even special-orthogonal nodes with b = -1 is lacking and is left for future work. This is load-bearing because Rule 3b prescribes decays of such b = -1 nodes, and the higher-rank examples in §5.1 and §5.2 rely on those admissibility decisions. Since the paper's own criterion for applicability is that the Coulomb branch has exactly one singular point (footnote 2 and §4.2), the absence of this analysis leaves open the possibility that some admitted b = -1 special-orthogonal nodes are bad in a stronger sense that changes the set of allowed decays.
  3. [§3, discussion of eq. (3.18)] The paper introduces an additional admissibility criterion when discussing eq. (3.18): a bad 4d class S theory is taken to imply that its 3d mirror quiver is bad and should be excluded from the Decay and Fission products. This criterion is used to eliminate the transition in eq. (3.18), and it is not derived from the 3d quiver data alone. Its validity outside the su(4) ~ so(6) class S setting is not assessed, yet it functions as an input to the algorithm whenever a candidate quiver is discarded on these grounds. The paper should either derive this criterion from the 3d perspective or explicitly state it as an additional conjecture with a precise domain of applicability.
  4. [§2, Figure 2.1 and eq. (2.9)] The algorithm does not decide which of its output quivers are redundant; converting the tentative diagram in Figure 2.1a into the Hasse diagram in Figure 2.1b uses the conjecture, stated after eq. (2.9), that two theories with identical Coulomb branch Hasse diagrams are different presentations of the same theory. The paper provides one Hilbert series check, eq. (2.9), and one Hasse-diagram comparison for the pair in eq. (3.12), but these do not establish the conjecture in general. Since the central claim is to 'systematically predict all descendant theories' and thereby determine the stratification, this conjecture is part of the algorithm's operating assumptions and should be formulated as a separate, explicitly flagged axiom.
minor comments (5)
  1. [§4.2] The sentence 'an alternative one for even special-orthogonal nodes is lacking' is grammatically unclear and should be reworded to something like 'an analogous analysis for even special-orthogonal nodes is lacking'.
  2. [§3] In the passage after eq. (3.19), 'only for n = 7, the theory we get is, in fact, free' is awkwardly phrased; consider rephrasing to clarify that for n = 7 the resulting theory is a free theory.
  3. [§2, eq. (2.4)] The balance calculation b = 4 * 5/4 + 5/8 - 5 for the central SO(6) node in eq. (2.4) relies on the distinction between the two USp(2) contribution cases in Rule 1; the text should state explicitly which USp(2) nodes are counted with 5/4 and which with 5/8, since the example is discussed before Rule 1 is formally introduced.
  4. [§2 and §6] The abstract and Section 6 say the algorithm applies to 'all orthosymplectic quivers', while the body restricts to simply-laced quivers with edge multiplicity one and excludes cases whose Coulomb branch symmetry involves g2 or f4; the scope statement should be consistent from the outset.
  5. [§5.1] The claim that the D-type orbi-instanton fission is 'the first time that an explicit example of this phenomenon was carried out beyond the g = su(K) case' would benefit from a brief comparison with the results of Ref. [37], which is cited but not discussed in relation to this claim.

Circularity Check

2 steps flagged · score 6.0 of 10

Partial circularity: the SO(6) balance coefficients (Rule 1) and the b=-1 decay rule (Rule 3b) are calibrated to class S and T_rho(SO(2N)) data that are then presented as successful benchmark outputs; out-of-sample applications remain non-circular.

  1. fitted input called prediction [Section 4.1 (Rule 1 calibration) vs Section 3 (validation)]
    "Reproducing the same behaviour from the balance notion for special-orthogonal theories of 2.2 requires that all the stand-alone U Sp(2) in the orthosymplectic construction must be effectively counted as contributing 5/8 -s towards Nf . ... In this section, we consider the Higgs branch of class S theories of types su(4) and so(6), and demonstrate that the algorithm of Section 2 produces the expected result."

    The 5/8 and 5/4 effective flavour contributions in Rule 1 are chosen precisely so that SO(6) quivers reproduce the unitary su(4) class S thresholds: good for n>8, balanced for n=8, bad for n<=7. Section 3 then benchmarks the algorithm against exactly these su(4)~so(6) class S theories and reports agreement. For this family, the agreement is built into the fitted coefficients, so the 'validation' is a consistency check of the interpolation rather than an independent prediction. The genuinely new applications (D-type orbi-instanton, higher-rank so(2N) class S) are not affected by this step.

  2. fitted input called prediction [Section 4.2 (Rule 3b derivation) vs Appendix A (T_rho(SO(16)) benchmark)]
    "The natural inclusion ordering on the closure of nilpotent orbits induces an ordering in the T_rho(SO(2N)) theories on the set of partitions rho-s associated with the orbits O-s. ... Applying the Orthosymplectic Decay and Fission algorithm yields the Coulomb branch Hasse diagram that is depicted in Figure A.1. We note that this reproduces the dominance ordering of the partitions associated to the nilpotent orbits rho, as desired."

    Rule 3b, which prescribes that b=-1 nodes decay by lowering rank by 1 with a c_n transverse slice, is read off from the nilpotent-orbit dominance ordering of T_rho(SO(2N)) theories in Section 4.2. Appendix A then showcases the algorithm on exactly such a theory, T_rho(SO(16)), and counts reproduction of the same dominance ordering as the successful output. The benchmark therefore re-uses the structural input from which the rule was extracted; it does not independently test Rule 3b, especially since the paper explicitly notes that a vacuum analysis for even special-orthogonal nodes with b=-1 is lacking.

full rationale

The paper contains two genuine circular steps. First, Rule 1's 5/8 and 5/4 balance contributions are fixed in Section 4.1 by matching the unitary su(4) class S good/balanced/bad thresholds, and Section 3 then validates the algorithm against exactly those su(4)~so(6) class S theories; the agreement there is a restatement of the fit. Second, Rule 3b is inferred from the nilpotent-orbit dominance ordering of T_rho(SO(2N)) theories in Section 4.2, and Appendix A benchmarks the algorithm on T_rho(SO(16)) by checking that it reproduces that same dominance ordering; again the test coincides with the input. These do not undermine the whole paper: the D-type orbi-instanton fission in (5.9)/(5.10) and the higher-rank so(2N) class S flows in Section 5.2 go beyond the fitted dataset, and the redundancy conjecture is explicitly flagged as a conjecture rather than hidden as an input. No load-bearing self-citation chain or imported uniqueness theorem was found; citations such as [21,22,35,54] provide background or prior constructions rather than forcing the central claim. The overall circularity is therefore partial: two benchmark families reduce by construction, while the genuinely new predictions keep the central claim from being entirely equivalent to its inputs.

Assumptions & free parameters 2 free parameters · 6 assumptions · 1 invented entities

The central claim rests on the empirical decay and fission rules, two fitted balance contributions, and one explicit conjecture about identical Hasse diagrams implying identical theories. No new physical entities are postulated; the fractional flavour contributions are bookkeeping devices. The su(4)~so(6) class S benchmark gives an external check, but the rules themselves are not derived from first principles.

free parameters (2)
  • USp(2) balance contribution to SO(6) node (stand-alone) = 5/8
    Rule 1; chosen so SO(6) with n USp(2) legs has balance (5n/8)-5, matching the known class S goodness threshold at n=8.
  • USp(2) balance contribution to SO(6) node (between SO(6) and SO(2)) = 5/4
    Rule 1; calibrated using class S theories with [2,2] and [3,1^3] punctures to reproduce the expected balance behavior.
assumptions (6)
  • ad hoc to paper The Orthosymplectic Decay and Fission rules (Rules 2-4) correctly describe all Coulomb branch Higgsings of simply-laced orthosymplectic quivers with edge multiplicity one.
    Used to produce every Hasse diagram in the paper; motivated by examples in Section 4 and validated on a subset of cases, but not proven.
  • ad hoc to paper Two quiver theories with identical Coulomb branch Hasse diagrams are different presentations of the same theory.
    Conjectured in Section 2 (discussion of Figure 2.1a); needed to remove redundant quivers and obtain the true Hasse diagram.
  • ad hoc to paper A bad 4d class S theory implies its 3d mirror quiver is bad and should be excluded from Decay and Fission products.
    Introduced in Section 3 via the Hall-Littlewood index for so(4) to rule out a specific transition; no independent 3d derivation is given.
  • domain assumption The magnetic quiver relation H_3/4/5/6d(E) = union_i C_3d(M_i) reliably maps Higgs branch RG flows to Coulomb branch stratifications.
    Standard assumption of the magnetic quiver programme, stated in Eq. (1.1) and used throughout Sections 3 and 5.
  • standard math su(4) is isomorphic to so(6) and maps nilpotent orbits as in Table 1.
    Classical Lie algebra isomorphism used to construct unitary and orthosymplectic realisations of the same class S theory (Section 3).
  • domain assumption For SO(6) nodes, the effect of half-integer lattice monopoles on goodness is fully captured by the effective balance renormalisation of Rule 1.
    Assumed in Section 2 and justified only in the class S context in Section 4.1; not proven for all quivers.
invented entities (1)
  • Effective fractional flavour contribution of USp(2) nodes attached to SO(6) nodes (5/8 or 5/4)
    purpose: Modify the balance formula so that half-integer lattice monopole effects on SO(6) nodes are captured by the local balance criterion.
    The numerical values are fitted to reproduce su(4)~so(6) class S goodness thresholds (Section 4.1); no independent falsifiable prediction outside the calibration examples is provided.

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Cite this review

Pith. "Pith review of A Pathway to Decay and Fission of Orthosymplectic Quiver Theories." pith.science (2026). https://pith.science/paper/TR6AKRQT

@misc{pith2026241215202,
  author       = {Pith},
  title        = {Pith review of: A Pathway to Decay and Fission of Orthosymplectic Quiver Theories},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TR6AKRQT}},
  note         = {Machine review of arXiv:2412.15202}
}
abstract

We present an algorithm to extract the Coulomb branch Hasse diagram of orthosymplectic 3d $\mathcal{N}=4$ quiver gauge theories. The algorithm systematically predicts all descendant theories arising from Coulomb branch Higgsing, thereby detailing the stratification of the symplectic singularity defined by the initial Coulomb branch. Leveraging the Lie algebra isomorphism $\mathfrak{su}(4) \cong \mathfrak{so}(6)$, we validate our algorithm via the 3d mirror of 4d theories of class $\mathcal{S}$ of such type. This comparison involves moduli spaces that admit both orthosymplectic and unitary quiver realisations, the latter being well-understood via standard techniques such as Decay and Fission. Higgsing on the Coulomb branch of the 3d mirror or magnetic quiver translates to Higgs branch renormalization group flows of the corresponding higher-dimensional SCFTs. Thus, we benchmark our method via Higgsing 6d $\mathcal{N}=(1,0)$ D-type orbi-instanton theories, predicting novel Higgsing patterns involving products of interacting fixed points, and class $\mathcal{S}$ theories of type $\mathfrak{so}(2N)$, demonstrating Higgsing to products of theories of types specified by Levi subalgebras of $\mathfrak{so}(2N)$.

Figures

Figures reproduced from arXiv: 2412.15202 by the authors.

Figure 2.1
Figure 2.1. (a) Tentative Hasse diagram for the Coulomb branch of the quiver 3d [PITH_FULL_IMAGE:figures/full_fig_p010_2_1.png] view at source ↗
Figure 3.1
Figure 3.1. 6 As we can see from [PITH_FULL_IMAGE:figures/full_fig_p012_3_1.png] view at source ↗
Figure 3.1
Figure 3.1. The star-shaped mirror dual quiver for the class [PITH_FULL_IMAGE:figures/full_fig_p013_3_1.png] view at source ↗
Figures from the paper (10 more)
Figure 3.2
Figure 3.2. Figure 3.2: The Hasse diagram under the dominance ordering on partitions of the nilpotent [PITH_FULL_IMAGE:figures/full_fig_p015_3_2.png]
Figure 3
Figure 3. Figure 3: b. This directly matches with the unitary quivers, as the Hasse diagrams for [PITH_FULL_IMAGE:figures/full_fig_p015_3.png]
Figure 3.3
Figure 3.3. Figure 3.3: All unitary 3d mirrors for the class S theories of type su(4) on a sphere with regular untwisted punctures and enhanced flavour symmetry. The partitions associated to the punctures can be read off from [PITH_FULL_IMAGE:figures/full_fig_p017_3_3.png]
Figure 3.4
Figure 3.4. Figure 3.4: Applying the unitary Decay and Fission algorithm to the quiver in equation (3.5) [PITH_FULL_IMAGE:figures/full_fig_p018_3_4.png]
Figure 3.5
Figure 3.5. Figure 3.5: There is one further subtlety in the derivation of the Hasse diagram in [PITH_FULL_IMAGE:figures/full_fig_p020_3_5.png]
Figure 3.5
Figure 3.5. Figure 3.5: Applying the Orthosymplectic Decay and Fission algorithm to the quiver on the [PITH_FULL_IMAGE:figures/full_fig_p022_3_5.png]
Figure 3
Figure 3. Figure 3: a, which also appears identically from the unitary Decay and Fission algorithm. [PITH_FULL_IMAGE:figures/full_fig_p024_3.png]
Figure 3.6
Figure 3.6. Figure 3.6: The Higgs branch Hasse diagram of Ssu4 ⟨C0,3⟩{[14], [14], [2, 12]} ∼= Sso6 ⟨C0,3⟩{[16], [16], [22, 12]} derived via Decay and Fission in (a) through the unitary 3d mirror and in (b) through the orthosymplectic 3d mirror [PITH_FULL_IMAGE:figures/full_fig_p025_3_6.png]
Figure 5.1
Figure 5.1. Figure 5.1: The M-theory configuration for a rank N (e8, gADE) orbi-instanton theory. whose string charge is given by the corresponding bold integer. There are also hypermulti￾plets, however the hypermultiplet spectrum is generally fixed by anomaly cancellation after the vector …
Figure 5.2
Figure 5.2. Figure 5.2: Some of the Higgs branch RG flows between class [PITH_FULL_IMAGE:figures/full_fig_p041_5_2.png]

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Forward citations

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