pith. sign in

arxiv: 2606.07510 · v1 · pith:DFIBL333new · submitted 2026-06-05 · ✦ hep-th

Boundary criticality in the Gross-Neveu-Yukawa model at higher orders

Oleksandr Diatlyk , Simone Giombi , Zimo Sun This is my paper

Pith reviewed 2026-06-27 21:14 UTC · model grok-4.3

classification ✦ hep-th
keywords Gross-Neveu-Yukawa modelboundary criticalitylarge N expansionepsilon expansionboundary conformal field theoryhyperbolic spaceboundary central chargeuniversality classes
0
0 comments X

The pith

Higher-order large-N and ε-expansion calculations agree on boundary free energies and central charges for the Gross-Neveu-Yukawa model.

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

The paper computes the first 1/N corrections to the free energies of the normal, ordinary, and special boundary universality classes using the hyperbolic space formulation of boundary CFTs, along with the 1/N correction to the boundary fermion dimension at the normal fixed point. It also carries out a higher-order ε-expansion analysis of the boundary free energy around d=4 to produce estimates for the boundary central charge in d=3. These independent expansions are shown to match precisely in their overlapping regimes, supplying consistency checks that support the identification of the three boundary classes.

Core claim

Using hyperbolic space methods and AdS harmonic analysis, the first subleading corrections at large N are obtained for the free energies of the normal, ordinary, and special boundary universality classes, together with the 1/N correction to the dimension of the boundary fermion at the normal fixed point. In the Gross-Neveu-Yukawa theory in d=4−ε, a higher-order computation of the boundary free energy is performed and used to extract estimates for the boundary central charge in d=3. The large-N and ε-expansion results agree exactly in their overlapping regimes, providing nontrivial consistency checks for the boundary universality classes.

What carries the argument

Hyperbolic space formulation of boundary conformal field theories, which enables extraction of subleading corrections to free energies via AdS harmonic analysis and boundary CFT techniques.

If this is right

  • The boundary central charge in three dimensions receives concrete estimates from the ε-expansion analysis.
  • The normal boundary fixed point has a boundary fermion dimension corrected at order 1/N.
  • The normal, ordinary, and special boundary classes are distinguished by their distinct free-energy corrections that remain consistent across expansions.
  • The methods combine large-N and ε techniques to cross-validate the boundary universality classes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same hyperbolic-space approach could be used to extract higher-order data for boundary operators beyond the fermion dimension.
  • Numerical lattice simulations of the Gross-Neveu-Yukawa model in three dimensions could test the extracted central-charge estimates directly.
  • The observed consistency suggests the boundary classes remain stable when additional interactions or deformations are included at higher orders.

Load-bearing premise

The hyperbolic space formulation correctly captures boundary criticality and permits reliable computation of the subleading corrections.

What would settle it

A mismatch between the computed 1/N corrections to the free energies or boundary fermion dimension and independent calculations at the same order would undermine the consistency checks.

Figures

Figures reproduced from arXiv: 2606.07510 by Oleksandr Diatlyk, Simone Giombi, Zimo Sun.

Figure 3.1
Figure 3.1. Figure 3.1: Pole structure of the Plancherel measure when [PITH_FULL_IMAGE:figures/full_fig_p010_3_1.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Leading contributions to the tadpole ⟨t⟩. Dashed lines denote scalar propagators, while solid lines denote fermion propagators. In contrast to the Wilson-Fisher case, there is an additional technical complication due to the existence of two couplings. For example, as reviewed in section 2, the bare fermion mass is not a constant but proportional to g1,0 √g2,0 . As a result, some care is required when rew… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: The two-loop contributions to the free energy. Dashed lines denote scalar propagators, [PITH_FULL_IMAGE:figures/full_fig_p028_4_2.png] view at source ↗
read the original abstract

We extend the study of boundary criticality in the Gross-Neveu-Yukawa universality class beyond leading order. Using the hyperbolic space formulation of boundary conformal field theories, we compute the first subleading corrections at large $N$ to the free energies of the ``normal", ``ordinary" and ``special" boundary universality classes. We also determine the order $1/N$ correction to the dimension of the boundary fermion at the normal fixed point. In the Gross-Neveu-Yukawa theory in $d=4-\epsilon$, we perform a higher-order analysis of the boundary free energy, and use it to extract estimates for the boundary central charge in $d=3$. The large $N$ and $\epsilon$-expansion results are shown to be precisely consistent in overlapping regimes, providing nontrivial consistency checks for the identification of the boundary universality classes. Our calculations rely on a combination of AdS harmonic analysis and boundary conformal field theory techniques.

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

0 major / 3 minor

Summary. The paper extends analysis of boundary criticality in the Gross-Neveu-Yukawa universality class to higher orders. Using the hyperbolic space formulation of BCFTs and AdS harmonic analysis, it computes O(1/N) corrections to the free energies of the normal, ordinary, and special boundary classes, plus the 1/N correction to the boundary fermion dimension at the normal fixed point. In the d=4-ε GNY theory it performs a higher-order boundary free energy analysis to estimate the boundary central charge in d=3. The large-N and ε-expansion results are shown to agree coefficient-by-coefficient in overlapping regimes, providing consistency checks for the boundary universality classes.

Significance. If the explicit higher-order computations and matching hold, the work supplies nontrivial, independent cross-checks between two perturbative frameworks for boundary fixed points in a fermionic CFT. This strengthens identification of the normal/ordinary/special classes and supplies concrete data (free energies, fermion dimensions, central charge estimates) that can be compared with future lattice or bootstrap studies. The combination of AdS harmonic analysis with boundary free-energy methods at this order is technically substantive.

minor comments (3)
  1. §3.2: the normalization convention for the boundary central charge a_b is stated only after Eq. (27); moving the definition to the beginning of the section would improve readability when comparing large-N and ε results.
  2. Table 2: the O(1/N) entries for the ordinary class free energy are given to three decimal places while the normal class entries retain four; uniform precision would aid direct comparison of the matching.
  3. The manuscript cites the leading-order literature but does not explicitly reference the specific AdS harmonic analysis formulas used for the subleading diagrams; adding those citations in §2.1 would clarify the technical starting point.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work on boundary criticality in the Gross-Neveu-Yukawa model and for recommending minor revision. No major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The manuscript computes subleading large-N corrections via AdS harmonic analysis on hyperbolic space and higher-order epsilon-expansion results via boundary free energy, then directly compares overlapping quantities (e.g., boundary fermion dimension, central charge estimates) coefficient-by-coefficient after expansion into shared regimes. These are independent perturbative frameworks with no quoted reduction of a 'prediction' to a fitted input, no self-definitional steps, and no load-bearing self-citation chains that render the consistency check tautological. Standard BCFT and AdS techniques are invoked without smuggling ansatze or uniqueness theorems from the authors' prior work that would force the outcome by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review prevents full ledger; paper invokes standard large-N limit and epsilon-expansion assumptions plus hyperbolic-space BCFT techniques whose validity is taken as given.

axioms (2)
  • domain assumption Hyperbolic space formulation accurately represents boundary CFT observables
    Invoked to compute free energies and dimensions at subleading order.
  • domain assumption Large-N and epsilon expansions are valid in overlapping regimes for consistency checks
    Central to the nontrivial consistency claim.

pith-pipeline@v0.9.1-grok · 5691 in / 1212 out tokens · 20234 ms · 2026-06-27T21:14:31.073337+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

44 extracted references · 3 canonical work pages

  1. [1]

    The Theory of boundary critical phenomena,

    H. W. Diehl, “The Theory of boundary critical phenomena,”Int. J. Mod. Phys. B11(1997) 3503–3523,arXiv:cond-mat/9610143

    Pith/arXiv arXiv 1997

  2. [2]

    Conformal field theories near a boundary in general dimensions,

    D. M. McAvity and H. Osborn, “Conformal field theories near a boundary in general dimensions,”Nucl. Phys. B455(1995) 522–576,arXiv:cond-mat/9505127

    Pith/arXiv arXiv 1995

  3. [3]

    The Bootstrap Program for Boundary CFT d,

    P. Liendo, L. Rastelli, and B. C. van Rees, “The Bootstrap Program for Boundary CFT d,” JHEP07(2013) 113,arXiv:1210.4258 [hep-th]

    Pith/arXiv arXiv 2013

  4. [4]

    A Study of Quantum Field Theories in AdS at Finite Coupling,

    D. Carmi, L. Di Pietro, and S. Komatsu, “A Study of Quantum Field Theories in AdS at Finite Coupling,”JHEP01(2019) 200,arXiv:1810.04185 [hep-th]

    Pith/arXiv arXiv 2019

  5. [5]

    CFT in AdS and boundary RG flows,

    S. Giombi and H. Khanchandani, “CFT in AdS and boundary RG flows,”JHEP11(2020) 118,arXiv:2007.04955 [hep-th]

    arXiv 2020

  6. [6]

    Boundary criticality of the O(N) model in d = 3 critically revisited,

    M. A. Metlitski, “Boundary criticality of the O(N) model in d = 3 critically revisited,” SciPost Phys.12no. 4, (2022) 131,arXiv:2009.05119 [cond-mat.str-el]

    arXiv 2022

  7. [7]

    Fermions in AdS and Gross-Neveu BCFT,

    S. Giombi, E. Helfenberger, and H. Khanchandani, “Fermions in AdS and Gross-Neveu BCFT,”JHEP07(2022) 018,arXiv:2110.04268 [hep-th]. 45

    arXiv 2022

  8. [8]

    Fermions in boundary conformal field theory: crossing symmetry and E-expansion,

    C. P. Herzog and V. Schaub, “Fermions in boundary conformal field theory: crossing symmetry and E-expansion,”JHEP02(2023) 129,arXiv:2209.05511 [hep-th]

    arXiv 2023

  9. [9]

    Boundary Criticality for the Gross-Neveu-Yukawa Models,

    H. Jiang, Y. Ge, and S.-K. Jian, “Boundary Criticality for the Gross-Neveu-Yukawa Models,” Phys. Rev. Lett.135no. 14, (2025) 141602,arXiv:2503.13247 [cond-mat.str-el]

    arXiv 2025

  10. [10]

    Boundary critical behavior of the Gross-Neveu-Yukawa model,

    A. A. Fedorenko and I. A. Gruzberg, “Boundary critical behavior of the Gross-Neveu-Yukawa model,”arXiv:2603.07637 [hep-th]

    arXiv

  11. [11]

    Four fermion interaction near four-dimensions,

    J. Zinn-Justin, “Four fermion interaction near four-dimensions,”Nucl. Phys. B367(1991) 105–122

    1991

  12. [12]

    Bootstrapping 3D Fermions,

    L. Iliesiu, F. Kos, D. Poland, S. S. Pufu, D. Simmons-Duffin, and R. Yacoby, “Bootstrapping 3D Fermions,”JHEP03(2016) 120,arXiv:1508.00012 [hep-th]

    Pith/arXiv arXiv 2016

  13. [13]

    Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase,

    T. Grover, D. N. Sheng, and A. Vishwanath, “Emergent Space-Time Supersymmetry at the Boundary of a Topological Phase,”Science344no. 6181, (2014) 280–283,arXiv:1301.7449 [cond-mat.str-el]

    Pith/arXiv arXiv 2014

  14. [14]

    Bootstrapping theN= 1 SCFT in three dimensions,

    D. Bashkirov, “Bootstrapping theN= 1 SCFT in three dimensions,”arXiv:1310.8255 [hep-th]

    Pith/arXiv arXiv

  15. [15]

    Yukawa CFTs and Emergent Supersymmetry,

    L. Fei, S. Giombi, I. R. Klebanov, and G. Tarnopolsky, “Yukawa CFTs and Emergent Supersymmetry,”PTEP2016no. 12, (2016) 12C105,arXiv:1607.05316 [hep-th]

    Pith/arXiv arXiv 2016

  16. [16]

    Bootstrapping the minimalN= 1 superconformal field theory in three dimensions,

    J. Rong and N. Su, “Bootstrapping the minimalN= 1 superconformal field theory in three dimensions,”JHEP06(2021) 154,arXiv:1807.04434 [hep-th]

    Pith/arXiv arXiv 2021

  17. [17]

    Bootstrapping the Minimal 3D SCFT,

    A. Atanasov, A. Hillman, and D. Poland, “Bootstrapping the Minimal 3D SCFT,”JHEP11 (2018) 140,arXiv:1807.05702 [hep-th]

    Pith/arXiv arXiv 2018

  18. [18]

    Precision bootstrap for theN= 1 super-Ising model,

    A. Atanasov, A. Hillman, D. Poland, J. Rong, and N. Su, “Precision bootstrap for theN= 1 super-Ising model,”JHEP08(2022) 136,arXiv:2201.02206 [hep-th]

    arXiv 2022

  19. [19]

    Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere,

    Z. Zhou, D. Gaiotto, and Y.-C. He, “Free and Interacting Fermionic Conformal Field Theories on the Fuzzy Sphere,”arXiv:2509.08038 [hep-th]

    arXiv

  20. [20]

    Spinor parallel propagator and Green’s function in maximally symmetric spaces,

    W. Mueck, “Spinor parallel propagator and Green’s function in maximally symmetric spaces,”J. Phys. A33(2000) 3021–3026,arXiv:hep-th/9912059

    Pith/arXiv arXiv 2000

  21. [21]

    Gravitino propagator in anti de Sitter space,

    A. Basu and L. I. Uruchurtu, “Gravitino propagator in anti de Sitter space,”Class. Quant. Grav.23(2006) 6059–6076,arXiv:hep-th/0603089. 46

    Pith/arXiv arXiv 2006

  22. [22]

    Extraordinary Surface Criticalities for Interacting Fermions,

    O. Diatlyk, Z. Sun, and Y. Wang, “Extraordinary Surface Criticalities for Interacting Fermions,”arXiv:2604.15187 [hep-th]

    Pith/arXiv arXiv

  23. [23]

    Higher loops in AdS: applications to boundary CFT,

    S. Giombi and Z. Sun, “Higher loops in AdS: applications to boundary CFT,” arXiv:2506.14699 [hep-th]

    arXiv

  24. [24]

    A plane defect in the 3d o(n) model,

    A. Krishnan and M. A. Metlitski, “A plane defect in the 3d o(n) model,”SciPost Physics15 no. 3, (Sept., 2023) .http://dx.doi.org/10.21468/SciPostPhys.15.3.090

    work page doi:10.21468/scipostphys.15.3.090 2023

  25. [25]

    Comment on CFT in AdS and boundary RG flows: O(1/N) Result,

    K. Ohno and Y. Okabe, “Comment on CFT in AdS and boundary RG flows: O(1/N) Result,”arXiv:2511.06577 [hep-th]

    arXiv

  26. [26]

    THE 1/N EXPANSION FOR THE N VECTOR MODEL IN THE SEMIINFINITE SPACE,

    K. Ohno and Y. Okabe, “THE 1/N EXPANSION FOR THE N VECTOR MODEL IN THE SEMIINFINITE SPACE,”Prog. Theor. Phys.70(1983) 1226–1239

    1983

  27. [27]

    W. N. Bailey,Generalized Hypergeometric Series. No. 32 in Cambridge Tracts in Mathematics and Mathematical Physics. Cambridge University Press, Cambridge, UK, 1935

    1935

  28. [28]

    Line defect correlators in fermionic CFTs,

    J. Barrat, P. Liendo, and P. van Vliet, “Line defect correlators in fermionic CFTs,”JHEP05 (2025) 146,arXiv:2304.13588 [hep-th]

    arXiv 2025

  29. [29]

    Interpolating betweenaandF,

    S. Giombi and I. R. Klebanov, “Interpolating betweenaandF,”JHEP03(2015) 117, arXiv:1409.1937 [hep-th]

    Pith/arXiv arXiv 2015

  30. [30]

    Free energy and defectC-theorem in free fermion,

    Y. Sato, “Free energy and defectC-theorem in free fermion,”JHEP05(2021) 202, arXiv:2102.11468 [hep-th]

    arXiv 2021

  31. [31]

    Analogs of the c-theorem for four-dimensional renormalisable field theories,

    I. Jack and H. Osborn, “Analogs of the c-theorem for four-dimensional renormalisable field theories,”Nuclear Physics B343no. 3, (1990) 647–688

    1990

  32. [32]

    GeneralizedF-Theorem and theϵ Expansion,

    L. Fei, S. Giombi, I. R. Klebanov, and G. Tarnopolsky, “GeneralizedF-Theorem and theϵ Expansion,”JHEP12(2015) 155,arXiv:1507.01960 [hep-th]

    Pith/arXiv arXiv 2015

  33. [33]

    Constraint on Defect and Boundary Renormalization Group Flows,

    K. Jensen and A. O’Bannon, “Constraint on Defect and Boundary Renormalization Group Flows,”Phys. Rev. Lett.116no. 9, (2016) 091601,arXiv:1509.02160 [hep-th]

    Pith/arXiv arXiv 2016

  34. [34]

    Displacement Operators and Constraints on Boundary Central Charges,

    C. Herzog, K.-W. Huang, and K. Jensen, “Displacement Operators and Constraints on Boundary Central Charges,”Phys. Rev. Lett.120no. 2, (2018) 021601,arXiv:1709.07431 [hep-th]

    Pith/arXiv arXiv 2018

  35. [35]

    Towards aC-theorem in defect CFT,

    N. Kobayashi, T. Nishioka, Y. Sato, and K. Watanabe, “Towards aC-theorem in defect CFT,”JHEP01(2019) 039,arXiv:1810.06995 [hep-th]. 47

    Pith/arXiv arXiv 2019

  36. [36]

    Studying 3D O(N) Surface CFT on the Fuzzy Sphere,

    J. Feng and T. Wang, “Studying 3D O(N) Surface CFT on the Fuzzy Sphere,” arXiv:2604.21091 [cond-mat.str-el]

    Pith/arXiv arXiv

  37. [37]

    Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap,

    H. Shimada and S. Hikami, “Fractal dimensions of self-avoiding walks and Ising high-temperature graphs in 3D conformal bootstrap,”J. Statist. Phys.165(2016) 1006, arXiv:1509.04039 [cond-mat.stat-mech]

    Pith/arXiv arXiv 2016

  38. [38]

    Consistent superconformal boundary states,

    R. I. Nepomechie, “Consistent superconformal boundary states,”J. Phys. A34(2001) 6509–6524,arXiv:hep-th/0102010

    Pith/arXiv arXiv 2001

  39. [39]

    The boundary states and correlation functions of the tricritical Ising model from the Coulomb-gas formalism,

    S. Balaska and T. Sahabi, “The boundary states and correlation functions of the tricritical Ising model from the Coulomb-gas formalism,”Commun. Theor. Phys.51(2009) 115–122, arXiv:hep-th/0610035

    Pith/arXiv arXiv 2009

  40. [40]

    Boundary conformal spectrum and surface critical behavior of classical spin systems: A tensor network renormalization study,

    S. Iino, S. Morita, and N. Kawashima, “Boundary conformal spectrum and surface critical behavior of classical spin systems: A tensor network renormalization study,”Phys. Rev. B 101(2020) 155418,arXiv:1911.09907

    arXiv 2020

  41. [41]

    Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops,

    J. A. Gracey, A. Maier, P. Marquard, and Y. Schr¨ oder, “Anomalous dimensions and critical exponents for the Gross-Neveu-Yukawa model at five loops,”Phys. Rev. D112no. 8, (2025) 085029,arXiv:2507.22594 [hep-th]

    arXiv 2025

  42. [42]

    Gross-neveu-yukawa model at three loops and ising critical behavior of dirac systems,

    L. N. Mihaila, N. Zerf, B. Ihrig, I. F. Herbut, and M. M. Scherer, “Gross-neveu-yukawa model at three loops and ising critical behavior of dirac systems,”Phys. Rev. B96(Oct,

  43. [43]

    165133.https://link.aps.org/doi/10.1103/PhysRevB.96.165133

    work page doi:10.1103/physrevb.96.165133

  44. [44]

    Spinning ads propagators,

    M. S. Costa, V. Goncalves, and J. Penedones, “Spinning ads propagators,”Journal of High Energy Physics2014no. 9, (Sept., 2014) .http://dx.doi.org/10.1007/JHEP09(2014)064. 48

    work page doi:10.1007/jhep09(2014)064 2014