pith. machine review for the scientific record. sign in

arxiv: 2604.15187 · v1 · submitted 2026-04-16 · ✦ hep-th

Recognition: unknown

Extraordinary Surface Criticalities for Interacting Fermions

Oleksandr Diatlyk , Zimo Sun , Yifan Wang
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:22 UTC · model grok-4.3

classification ✦ hep-th
keywords surface defectsGross-Neveu-Yukawa modelrenormalization group flowsfermionic anomaliessurface critical phenomenadefect conformal field theorytopological structuresgeometric structures in coupling space
0
0 comments X

The pith

Certain defect renormalization group flows in the three-dimensional Gross-Neveu-Yukawa model admit exact infrared solutions that encode fermionic anomalies in surface dynamics.

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

The paper studies surface critical phenomena in systems of interacting fermions by analyzing the three-dimensional Gross-Neveu-Yukawa model. It identifies a class of defect renormalization group flows that reach exact infrared fixed points. At these fixed points the surface dynamics directly incorporate the effects of fermionic anomalies. The analysis also reveals topological and geometric patterns that arise in the space of possible defect couplings. A reader would care because exact control over these surface criticalities offers a window into phenomena that are otherwise accessible only through approximation or numerical methods.

Core claim

In the three-dimensional Gross-Neveu-Yukawa model, a class of defect renormalization group flows possesses exact infrared solutions. These solutions encode fermionic anomalies within the resulting surface dynamics. The space of defect couplings exhibits emergent topological and geometric structures, which the authors relate to a defect analogue of the CFT distance conjecture.

What carries the argument

defect renormalization group flows in the Gross-Neveu-Yukawa model, which reach exact infrared fixed points where anomalies appear in surface dynamics and geometric structures emerge in coupling space

Load-bearing premise

The renormalization group flows in the defect setup of the 3D Gross-Neveu-Yukawa model permit exact infrared solutions that encode the anomalies without requiring numerical or approximate methods.

What would settle it

A lattice Monte Carlo simulation of the three-dimensional Gross-Neveu-Yukawa model with chosen surface defects that produces infrared fixed-point values or anomaly coefficients inconsistent with the exact solutions would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.15187 by Oleksandr Diatlyk, Yifan Wang, Zimo Sun.

Figure 1
Figure 1. Figure 1: FIG. 1. The extraordinary surface defect viewed as a squeezed limit [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Emergent conformal manifold of extraordinary surface de [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Fusion of normal surface defects in the GNY CFT into the extraordinary surface defect, shown in the bottom diagrams. This fusion [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
read the original abstract

Interacting fermions exhibit a rich landscape of surface defects and associated critical phenomena. We investigate novel surface critical behavior in the three-dimensional Gross-Neveu-Yukawa model. For a class of defect renormalization group flows, we obtain exact infrared solutions and show how fermionic anomalies are encoded in the resulting surface dynamics. We further uncover emergent topological and geometric structures in the defect coupling space, and comment on their relation to a defect analogue of the CFT distance conjecture.

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

1 major / 1 minor

Summary. The manuscript examines novel surface critical behavior in the three-dimensional Gross-Neveu-Yukawa model. For a class of defect renormalization group flows, it obtains exact infrared solutions and shows how fermionic anomalies are encoded in the resulting surface dynamics. It further identifies emergent topological and geometric structures in the defect coupling space and comments on their relation to a defect analogue of the CFT distance conjecture.

Significance. If the exact IR solutions and anomaly encoding hold without fine-tuning, the work would offer valuable benchmarks for defect CFTs in interacting fermionic systems, where exact results are rare. The emergent structures and distance-conjecture link could stimulate further exploration of geometric aspects of defects, complementing bulk CFT studies.

major comments (1)
  1. [Section on defect RG flows and exact IR solutions] The exact IR solutions are derived within a reduced subspace of defect couplings. The manuscript must demonstrate that these fixed points are attractive (or that the subspace is reached without fine-tuning) under generic perturbations in the full defect coupling space; otherwise the claimed surface criticalities and anomaly encoding would not be realized in generic flows. This stability analysis is load-bearing for the central claims.
minor comments (1)
  1. [Introduction] The abstract and introduction could include a brief comparison to prior work on surface defects in the GNY model to better contextualize the novelty of the exact solutions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: The exact IR solutions are derived within a reduced subspace of defect couplings. The manuscript must demonstrate that these fixed points are attractive (or that the subspace is reached without fine-tuning) under generic perturbations in the full defect coupling space; otherwise the claimed surface criticalities and anomaly encoding would not be realized in generic flows. This stability analysis is load-bearing for the central claims.

    Authors: We appreciate the referee highlighting this point. Our work explicitly considers a class of defect renormalization group flows that admit exact infrared solutions, as stated in the abstract and throughout the manuscript. The claims regarding surface criticalities, anomaly encoding, and emergent structures are made within this class and do not assert that the fixed points are reached or stable under generic perturbations in the full defect coupling space. We will revise the manuscript to more explicitly delineate the scope of our results and to motivate the physical relevance of the reduced subspace (e.g., via symmetry constraints or specific lattice realizations that naturally restrict the defect couplings). A complete stability analysis in the unrestricted space would require the full set of beta functions outside the subspace, which are not known exactly and lie beyond the present exact-solution approach. revision: partial

Circularity Check

0 steps flagged

No significant circularity; exact IR solutions derived from RG equations without reduction to inputs

full rationale

The paper obtains exact infrared solutions by solving the defect renormalization group flows in the 3D Gross-Neveu-Yukawa model, then extracts anomaly encoding and emergent structures in coupling space. No quoted steps reduce a prediction to a fitted parameter by construction, invoke self-citations as load-bearing uniqueness theorems, or smuggle ansatze. The derivation chain remains self-contained against the model's beta functions and anomaly matching, with the CFT distance conjecture comment appearing as an interpretive remark rather than a foundational assumption. This is the expected outcome for an analytic RG study.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on abstract; no explicit free parameters, new entities, or ad-hoc axioms mentioned beyond the standard Gross-Neveu-Yukawa model.

axioms (1)
  • domain assumption The three-dimensional Gross-Neveu-Yukawa model is a valid effective description for the interacting fermions and surface defects under study.
    The model is invoked as the starting point for the defect RG analysis.

pith-pipeline@v0.9.0 · 5362 in / 1139 out tokens · 64230 ms · 2026-05-10T10:22:24.385489+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 1 Pith paper

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

  1. A Twist on Scattering from Defect Anomalies

    hep-th 2026-05 unverdicted novelty 7.0

    Defect 't Hooft anomalies trap charges at symmetry-line junctions and thereby drive categorical scattering into twist operators.

Reference graph

Works this paper leans on

124 extracted references · 83 canonical work pages · cited by 1 Pith paper

  1. [1]

    −γ1/¯x12 2µ±tanh( r 2) cosh( r 2) , (III.11) 5 wherer≡arccosh(v)andG ± satisfy the boundary condition γ1G±(x1, x2) z1→0 =∓G ±(x1, x2)|z1→0 .(III.12) The fermion propagatorsG 11 andG 12 can be expressed as linear combinations ofG ±, with coefficients fixed by the bulk conformal block expansion. According to [26], for a bulk op- erator of dimension∆, there ...

  2. [2]

    So theb-anomaly of the factorized defect|B 1⟩⟨B1|isb |B1⟩⟨B1| =− N 4

    = N 12 log(R)from (III.17). So theb-anomaly of the factorized defect|B 1⟩⟨B1|isb |B1⟩⟨B1| =− N 4 . On the other hand, theb-anomaly of a single 2dchiral Majo- rana fermion is cL+cR 2 = 1

  3. [3]

    In Appendix D 3, we find that the orderN 0 contribution in b|B1⟩⟨B1| is equal to− 9

    Therefore, the combined sys- tem|B 1⟩⟨B1|+χ I has a vanishingb-anomaly at orderN, which is the same as other points on the conformal manifold. In Appendix D 3, we find that the orderN 0 contribution in b|B1⟩⟨B1| is equal to− 9

  4. [4]

    Letψ I L andψ I R be the dimension 3 2 boundary fermions in the two decouple|B 1⟩boundaries

    So the proposal (I.3) obeys the de- fectb-theoremb UV > bIR at theN 0 order sinceb UV = 0. Letψ I L andψ I R be the dimension 3 2 boundary fermions in the two decouple|B 1⟩boundaries. We identify the marginal operator that decouples fromϕ e atµ= 1 2 as Oe = 1√ 2N (ψI L +ψ I R)χI .(IV .1) Similarly, the marginal operator that decouples fromϕ o at µ= 1 2 is...

  5. [5]

    A. J. Bray and M. A. Moore, J. Phys. A10, 1927 (1977)

    1927

  6. [6]

    D. M. McAvity and H. Osborn, Nucl. Phys. B455, 522 (1995), arXiv:cond-mat/9505127

    work page Pith review arXiv 1995

  7. [7]

    Cardy,Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, 1996)

    J. Cardy,Scaling and Renormalization in Statistical Physics, Cambridge Lecture Notes in Physics (Cambridge University Press, 1996)

    1996

  8. [8]

    H. W. Diehl, Int. J. Mod. Phys. B11, 3503 (1997), arXiv:cond- mat/9610143

    work page arXiv 1997

  9. [9]

    M. A. Metlitski, SciPost Phys.12, 131 (2022), arXiv:2009.05119 [cond-mat.str-el]

    work page arXiv 2022

  10. [10]

    CFT in AdS and boundary RG flows,

    S. Giombi and H. Khanchandani, JHEP11, 118 (2020), arXiv:2007.04955 [hep-th]

    work page arXiv 2020

  11. [11]

    Padayasi, A

    J. Padayasi, A. Krishnan, M. A. Metlitski, I. A. Gruzberg, and M. Meineri, SciPost Phys.12, 190 (2022), arXiv:2111.03071 [cond-mat.stat-mech]

    work page arXiv 2022

  12. [12]

    F. P. Toldin and M. A. Metlitski, Phys. Rev. Lett.128, 215701 (2022), arXiv:2111.03613 [cond-mat.stat-mech]

    work page arXiv 2022

  13. [13]

    Krishnan and M

    A. Krishnan and M. A. Metlitski, SciPost Phys.15, 090 (2023), arXiv:2301.05728 [cond-mat.str-el]

    work page arXiv 2023

  14. [14]

    Surface defects in the O(N ) model,

    M. Tr ´epanier, JHEP09, 074 (2023), arXiv:2305.10486 [hep- th]

    work page arXiv 2023

  15. [15]

    Notes on a surface defect in the O(N ) model,

    S. Giombi and B. Liu, JHEP12, 004 (2023), arXiv:2305.11402 [hep-th]

    work page arXiv 2023

  16. [16]

    Phases of surface defects in scalar field theories,

    A. Raviv-Moshe and S. Zhong, JHEP08, 143 (2023), arXiv:2305.11370 [hep-th]

    work page arXiv 2023

  17. [17]

    Diatlyk, Z

    O. Diatlyk, Z. Sun, and Y . Wang, (2024), arXiv:2411.16522 [hep-th]

    work page arXiv 2024

  18. [18]

    F. K. Popov and Y . Wang, (2025), arXiv:2504.06203 [hep-th]

    work page arXiv 2025

  19. [19]

    Fer mionic Symmetry Protected Topological Phases and Cobordisms,

    A. Kapustin, R. Thorngren, A. Turzillo, and Z. Wang, JHEP 12, 052 (2015), arXiv:1406.7329 [cond-mat.str-el]

    work page arXiv 2015

  20. [20]

    Fermion Path Integrals And Topological Phases

    E. Witten, Rev. Mod. Phys.88, 035001 (2016), arXiv:1508.04715 [cond-mat.mes-hall]

    work page Pith review arXiv 2016

  21. [21]

    Gapped Boundary Phases of Topological Insulators via Weak Coupling,

    N. Seiberg and E. Witten, PTEP2016, 12C101 (2016), arXiv:1602.04251 [cond-mat.str-el]

    work page arXiv 2016

  22. [22]

    D. S. Freed and M. J. Hopkins, Geom. Topol.25, 1165 (2021), arXiv:1604.06527 [hep-th]

    work page arXiv 2021

  23. [23]

    Witten, Phys

    E. Witten, Phys. Rev. B94, 195150 (2016), arXiv:1605.02391 [hep-th]

    work page arXiv 2016

  24. [24]

    Jackiw and C

    R. Jackiw and C. Rebbi, Phys. Rev. D13, 3398 (1976)

    1976

  25. [25]

    C. G. Callan, Jr. and J. A. Harvey, Nucl. Phys. B250, 427 (1985)

    1985

  26. [26]

    Seiberg, T

    N. Seiberg, T. Senthil, C. Wang, and E. Witten, Annals Phys. 374, 395 (2016), arXiv:1606.01989 [hep-th]

    work page arXiv 2016

  27. [27]

    M. A. Metlitski, A. Vishwanath, and C. Xu, Phys. Rev. B95, 205137 (2017), arXiv:1611.05049 [cond-mat.str-el]

    work page arXiv 2017

  28. [28]

    Defect Anomalies, a Spin-Flux Duality, and Boson-Kondo Problems,

    Z. Komargodski, F. K. Popov, and B. C. Rayhaun, (2025), arXiv:2508.14963 [hep-th]

    work page arXiv 2025

  29. [29]

    Giombi, E

    S. Giombi, E. Helfenberger, and H. Khanchandani, JHEP07, 018 (2022), arXiv:2110.04268 [hep-th]

    work page arXiv 2022

  30. [30]

    C. P. Herzog and V . Schaub, JHEP02, 129 (2023), arXiv:2209.05511 [hep-th]

    work page arXiv 2023

  31. [31]

    Giombi, E

    S. Giombi, E. Helfenberger, and H. Khanchandani, JHEP08, 224 (2023), arXiv:2211.11073 [hep-th]

    work page arXiv 2023

  32. [32]

    Jiang, Y

    H. Jiang, Y . Ge, and S.-K. Jian, Phys. Rev. Lett.135, 141602 (2025), arXiv:2503.13247 [cond-mat.str-el]

    work page arXiv 2025

  33. [33]

    A. A. Fedorenko and I. A. Gruzberg, (2026), arXiv:2603.07637 [hep-th]

    work page arXiv 2026

  34. [34]

    Iliesiu, F

    L. Iliesiu, F. Kos, D. Poland, S. S. Pufu, D. Simmons-Duffin, and R. Yacoby, JHEP03, 120 (2016), arXiv:1508.00012 [hep- th]

    work page arXiv 2016

  35. [35]

    R. S. Erramilli, L. V . Iliesiu, P. Kravchuk, A. Liu, D. Poland, and D. Simmons-Duffin, JHEP02, 036 (2023), arXiv:2210.02492 [hep-th]

    work page arXiv 2023

  36. [36]

    M. S. Mitchell and D. Poland, JHEP09, 134 (2024), arXiv:2406.12974 [hep-th]

    work page arXiv 2024

  37. [37]

    L. Fei, S. Giombi, I. R. Klebanov, and G. Tarnopolsky, PTEP 2016, 12C105 (2016), arXiv:1607.05316 [hep-th]

    work page arXiv 2016

  38. [38]

    N. Zerf, L. N. Mihaila, P. Marquard, I. F. Herbut, and M. M. Scherer, Phys. Rev. D96, 096010 (2017), arXiv:1709.05057 [hep-th]

    work page arXiv 2017

  39. [39]

    J. A. Gracey, A. Maier, P. Marquard, and Y . Schr ¨oder, Phys. Rev. D112, 085029 (2025), arXiv:2507.22594

    work page arXiv 2025

  40. [40]

    J. A. Gracey, Int. J. Mod. Phys. A6, 395 (1991), [Erratum: Int.J.Mod.Phys.A 6, 2755 (1991)]

    1991

  41. [41]

    J. A. Gracey, Phys. Lett. B297, 293 (1992)

    1992

  42. [42]

    A. N. Vasil’ev, S. E. Derkachov, N. A. Kivel, and A. S. Stepanenko, Theor. Math. Phys.94, 127 (1993), arXiv:hep- th/9302034

    work page arXiv 1993

  43. [43]

    J. A. Gracey, Int. J. Mod. Phys. A9, 727 (1994), arXiv:hep- th/9306107

    work page arXiv 1994

  44. [44]

    Diatlyk, Z

    O. Diatlyk, Z. Sun, and Y . Wang, (2026), to appear

    2026

  45. [45]

    The ordinary surface defect of the GNY model,

    O. Diatlyk, Z. Sun, and Y . Wang, “The ordinary surface defect of the GNY model,” (2026), to appear

    2026

  46. [46]

    For example, a non-genuine ’t Hooft loop in4dSU(N)gauge theory can be viewed as a mon- odromy defect for theZ N electric one-form symmetry

    Usual monodromy defects are defined for0-form symmetries, but their extension top-form symmetries is straightforward: they correspond to localized flux insertions for the associated background gauge fields. For example, a non-genuine ’t Hooft loop in4dSU(N)gauge theory can be viewed as a mon- odromy defect for theZ N electric one-form symmetry. The novelt...

  47. [47]

    A Constraint on Defect and Boundary Renormalization Group Flows

    K. Jensen and A. O’Bannon, Phys. Rev. Lett.116, 091601 (2016), arXiv:1509.02160 [hep-th]

    work page Pith review arXiv 2016

  48. [48]

    Casini, I

    H. Casini, I. Salazar Landea, and G. Torroba, JHEP04, 166 (2019), arXiv:1812.08183 [hep-th]

    work page arXiv 2019

  49. [49]

    Wang, JHEP11, 122 (2021), arXiv:2012.06574 [hep-th]

    Y . Wang, JHEP11, 122 (2021), arXiv:2012.06574 [hep-th]

    work page arXiv 2021

  50. [50]

    Shachar, R

    T. Shachar, R. Sinha, and M. Smolkin, SciPost Phys.15, 240 (2023), arXiv:2212.08081 [hep-th]

    work page arXiv 2023

  51. [51]

    On the Geometry of the String Landscape and the Swampland

    H. Ooguri and C. Vafa, Nucl. Phys. B766, 21 (2007), arXiv:hep-th/0605264

    work page Pith review arXiv 2007

  52. [52]

    Ooguri and Y

    H. Ooguri and Y . Wang, JHEP12, 154 (2024), arXiv:2405.00674 [hep-th]

    work page arXiv 2024

  53. [53]

    Grover, D.N

    T. Grover, D. N. Sheng, and A. Vishwanath, Science344, 280 (2014), arXiv:1301.7449 [cond-mat.str-el]

    work page arXiv 2014

  54. [54]

    Rong and N

    J. Rong and N. Su, JHEP06, 154 (2021), arXiv:1807.04434 [hep-th]

    work page arXiv 2021

  55. [55]

    Atanasov, A

    A. Atanasov, A. Hillman, and D. Poland, JHEP11, 140 (2018), arXiv:1807.05702 [hep-th]

    work page arXiv 2018

  56. [56]

    Atanasov, A

    A. Atanasov, A. Hillman, D. Poland, J. Rong, and N. Su, JHEP08, 136 (2022), arXiv:2201.02206 [hep-th]

    work page arXiv 2022

  57. [57]

    Gukov, V

    S. Gukov, V . Krushkal, L. Meier, and D. Pei, (2025), arXiv:2509.12402 [math.AT]

    work page arXiv 2025

  58. [58]

    Cuomo and S

    G. Cuomo and S. Zhang, JHEP03, 022 (2024), arXiv:2306.00085 [hep-th]

    work page arXiv 2024

  59. [59]

    The extraordinary-log scenario in theO(N)Wilson-Fisher theory [9, 54] does not appear to happen here as in confirmed 9 by our direct largeNanalysis in Section III

  60. [60]

    In fact, the phase diagram ofO(N)-invariant boundaries in the GNY model as presented in [25] is incomplete ind= 3. In particular, there is in addition, another extraordinary bound- ary universality class with decoupled fermions, much like the extraordinary surface defect considered here; furthermore, the special and ordinary boundaries disappear at a crit...

  61. [61]

    Boundary criticality in the GNY model at higher orders,

    O. Diatlyk, S. Giombi, and Z. Sun, “Boundary criticality in the GNY model at higher orders,” (2026), to appear

    2026

  62. [62]

    Thorngren and Y

    R. Thorngren and Y . Wang, JHEP09, 017 (2021), arXiv:2012.15861 [hep-th]

    work page arXiv 2021

  63. [63]

    A. N. Redlich, Phys. Rev. D29, 2366 (1984)

    1984

  64. [64]

    A. J. Niemi and G. W. Semenoff, Phys. Rev. Lett.51, 2077 (1983)

    2077

  65. [65]

    Alvarez-Gaume, S

    L. Alvarez-Gaume, S. Della Pietra, and G. W. Moore, Annals Phys.163, 288 (1985)

    1985

  66. [66]

    Córdova, D.S

    C. C ´ordova, D. S. Freed, H. T. Lam, and N. Seiberg, SciPost Phys.8, 001 (2020), arXiv:1905.09315 [hep-th]

    work page arXiv 2020

  67. [67]

    Hason, Z

    I. Hason, Z. Komargodski, and R. Thorngren, SciPost Phys. 8, 062 (2020), arXiv:1910.14039 [hep-th]

    work page arXiv 2020

  68. [68]

    Any3dspin QFT is defined up to a quantized Chern-Simons counter-termkCS g withk∈Zwhich modifies the contact terms in the stress-tensor two-point functions and shifts the boundary gravitational anomaly [45, 87–89] but this effect is canceled between one boundary|B⟩and its transverse reflec- tion⟨B|

  69. [69]

    This fixes the Chern-Simons counterterm in the previous footnote

    Here the constant shift inρis fixed by requiringρ(0) = 1/2 so that the anomaly theory (II.7) isT-invariant [90]. This fixes the Chern-Simons counterterm in the previous footnote

  70. [70]

    Zinn-Justin, Nucl

    J. Zinn-Justin, Nucl. Phys. B367, 105 (1991)

    1991

  71. [71]

    See Appendix B for relevant three-point functions

    In contrast, the deformationhϕ 2δ(z)is marginal but not ex- actly marginal in the largeNlimit [41]. See Appendix B for relevant three-point functions

  72. [72]

    The 1 N anomalous dimensions is positive for the fermions and negative for the pseudoscalar

    The fermion and pseudoscalar fields all have dimension∆ = 1in the largeNlimit. The 1 N anomalous dimensions is positive for the fermions and negative for the pseudoscalar. [36, 39]

  73. [73]

    Mueck, J

    W. Mueck, J. Phys. A33, 3021 (2000), arXiv:hep-th/9912059

    work page arXiv 2000

  74. [74]

    Basu and L

    A. Basu and L. I. Uruchurtu, Class. Quant. Grav.23, 6059 (2006), arXiv:hep-th/0603089

    work page arXiv 2006

  75. [75]

    A new logarithmic solution emerges at this point and is given by∂ µ(G+ −G −)|µ=1/2

    The two solutionsG ± in (III.11) are degenerate atµ= 1/2 where the fermionic Breitenlohner-Freedman (BF) bound in AdS3 is saturated. A new logarithmic solution emerges at this point and is given by∂ µ(G+ −G −)|µ=1/2. While its lead- ing fall-off at largercorresponds to a ˆ∆ = 1/2boundary fermion, this solution is not normalizable [91]. This is another ind...

  76. [76]

    In our normalization, this free fermion propagator is − /x12 4π|x12|3

  77. [77]

    Kontsevich and Y

    M. Kontsevich and Y . Soibelman, inKIAS Annual Interna- tional Conference on Symplectic Geometry and Mirror Sym- metry(2000) pp. 203–263, arXiv:math/0011041

    work page arXiv 2000

  78. [78]

    Roggenkamp and K

    D. Roggenkamp and K. Wendland, Commun. Math. Phys. 251, 589 (2004), arXiv:hep-th/0308143

    work page arXiv 2004

  79. [79]

    Soibelman, (2025), arXiv:2506.00896 [hep-th]

    Y . Soibelman, (2025), arXiv:2506.00896 [hep-th]

    work page arXiv 2025

  80. [80]

    Alternatively, one can derive the relation betweenµandsby computing the anomalous dimension ofψ I L/R under this per- turbation and matching it with the boundary dimension ofΨ I e. This requires the boundary fermion four-point function at or- der1/Nfor the normal boundary condition, analogous to the boundary four-point functions studied in the largeNexpan...

Showing first 80 references.