Abstract
We study the boundary critical behavior of conformal field theories of interacting fermions in the Gross-Neveu universality class. By a Weyl transformation, the problem can be studied by placing the CFT in an anti de Sitter space background. After reviewing some aspects of free fermion theories in AdS, we use both large N methods and the epsilon expansion near 2 and 4 dimensions to study the conformal boundary conditions in the Gross-Neveu CFT. At large N and general dimension d, we find three distinct boundary conformal phases. Near four dimensions, where the CFT is described by the Wilson-Fisher fixed point of the Gross-Neveu-Yukawa model, two of these phases correspond respectively to the choice of Neumann or Dirichlet boundary condition on the scalar field, while the third one corresponds to the case where the bulk scalar field acquires a classical expectation value. One may flow between these boundary critical points by suitable relevant boundary deformations. We compute the AdS free energy on each of them, and verify that its value is consistent with the boundary version of the F-theorem. We also compute some of the BCFT observables in these theories, including bulk two-point functions of scalar and fermions, and four-point functions of boundary fermions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D.M. McAvity and H. Osborn, Conformal field theories near a boundary in general dimensions, Nucl. Phys. B 455 (1995) 522 [cond-mat/9505127] [INSPIRE].
M. Billò, V. Gonçalves, E. Lauria and M. Meineri, Defects in conformal field theory, JHEP 04 (2016) 091 [arXiv:1601.02883] [INSPIRE].
H.W. Diehl, The Theory of boundary critical phenomena, Int. J. Mod. Phys. B 11 (1997) 3503 [cond-mat/9610143] [INSPIRE].
P. Liendo, L. Rastelli and B.C. van Rees, The Bootstrap Program for Boundary CFTd, JHEP 07 (2013) 113 [arXiv:1210.4258] [INSPIRE].
D. Carmi, L. Di Pietro and S. Komatsu, A Study of Quantum Field Theories in AdS at Finite Coupling, JHEP 01 (2019) 200 [arXiv:1810.04185] [INSPIRE].
S. Giombi and H. Khanchandani, CFT in AdS and boundary RG flows, JHEP 11 (2020) 118 [arXiv:2007.04955] [INSPIRE].
D.M. McAvity and H. Osborn, Energy momentum tensor in conformal field theories near a boundary, Nucl. Phys. B 406 (1993) 655 [hep-th/9302068] [INSPIRE].
C.P. Herzog and K.-W. Huang, Boundary Conformal Field Theory and a Boundary Central Charge, JHEP 10 (2017) 189 [arXiv:1707.06224] [INSPIRE].
C.P. Herzog, K.-W. Huang, I. Shamir and J. Virrueta, Superconformal Models for Graphene and Boundary Central Charges, JHEP 09 (2018) 161 [arXiv:1807.01700] [INSPIRE].
D.J. Gross and A. Neveu, Dynamical Symmetry Breaking in Asymptotically Free Field Theories, Phys. Rev. D 10 (1974) 3235 [INSPIRE].
M. Moshe and J. Zinn-Justin, Quantum field theory in the large N limit: A Review, Phys. Rept. 385 (2003) 69 [hep-th/0306133] [INSPIRE].
S. Giombi, Higher Spin — CFT Duality, in Theoretical Advanced Study Institute in Elementary Particle Physics: New Frontiers in Fields and Strings, (2017), pp. 137–214, DOI [arXiv:1607.02967] [INSPIRE].
M.F. Paulos, J. Penedones, J. Toledo, B.C. van Rees and P. Vieira, The S-matrix bootstrap. Part I: QFT in AdS, JHEP 11 (2017) 133 [arXiv:1607.06109] [INSPIRE].
C.P. Herzog and I. Shamir, On Marginal Operators in Boundary Conformal Field Theory, JHEP 10 (2019) 088 [arXiv:1906.11281] [INSPIRE].
C.P. Herzog and N. Kobayashi, The O(N) model with ϕ6 potential in ℝ2 × ℝ+, JHEP 09 (2020) 126 [arXiv:2005.07863] [INSPIRE].
C.G. Callan, and F. Wilczek, Infrared behavior at negative curvature, Nucl. Phys. B 340 (1990) 366 [INSPIRE].
O. Aharony, D. Marolf and M. Rangamani, Conformal field theories in anti-de Sitter space, JHEP 02 (2011) 041 [arXiv:1011.6144] [INSPIRE].
O. Aharony, M. Berkooz, A. Karasik and T. Vaknin, Supersymmetric field theories on AdSp × Sq, JHEP 04 (2016) 066 [arXiv:1512.04698] [INSPIRE].
M. Hogervorst, M. Meineri, J. Penedones and K.S. Vaziri, Hamiltonian truncation in Anti-de Sitter spacetime, JHEP 08 (2021) 063 [arXiv:2104.10689] [INSPIRE].
A. Antunes, M.S. Costa, J. Penedones, A. Salgarkar and B.C. van Rees, Towards bootstrapping RG flows: sine-Gordon in AdS, JHEP 12 (2021) 094 [arXiv:2109.13261] [INSPIRE].
M. Henneaux, Boundary terms in the AdS/CFT correspondence for spinor fields, in International Meeting on Mathematical Methods in Modern Theoretical Physics (ISPM 98), (1998), pp. 161–170 [hep-th/9902137] [INSPIRE].
W. Mueck and K.S. Viswanathan, Conformal field theory correlators from classical field theory on anti-de Sitter space. 2. Vector and spinor fields, Phys. Rev. D 58 (1998) 106006 [hep-th/9805145] [INSPIRE].
G.E. Arutyunov and S.A. Frolov, On the origin of supergravity boundary terms in the AdS/CFT correspondence, Nucl. Phys. B 544 (1999) 576 [hep-th/9806216] [INSPIRE].
W. Mueck, Spinor parallel propagator and Green’s function in maximally symmetric spaces, J. Phys. A 33 (2000) 3021 [hep-th/9912059] [INSPIRE].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
T. Kawano and K. Okuyama, Spinor exchange in AdS(d + 1), Nucl. Phys. B 565 (2000) 427 [hep-th/9905130] [INSPIRE].
A. Basu and L.I. Uruchurtu, Gravitino propagator in anti de Sitter space, Class. Quant. Grav. 23 (2006) 6059 [hep-th/0603089] [INSPIRE].
R. Aros and D.E. Diaz, Determinant and Weyl anomaly of Dirac operator: a holographic derivation, J. Phys. A 45 (2012) 125401 [arXiv:1111.1463] [INSPIRE].
J. Faller, S. Sarkar and M. Verma, Mellin Amplitudes for Fermionic Conformal Correlators, JHEP 03 (2018) 106 [arXiv:1711.07929] [INSPIRE].
M. Nishida and K. Tamaoka, Fermions in Geodesic Witten Diagrams, JHEP 07 (2018) 149 [arXiv:1805.00217] [INSPIRE].
J. Zinn-Justin, Four fermion interaction near four-dimensions, Nucl. Phys. B 367 (1991) 105 [INSPIRE].
L. Fei, S. Giombi, I.R. Klebanov and G. Tarnopolsky, Yukawa CFTs and Emergent Supersymmetry, PTEP 2016 (2016) 12C105 [arXiv:1607.05316] [INSPIRE].
S. Giombi and I.R. Klebanov, Interpolating between a and F , JHEP 03 (2015) 117 [arXiv:1409.1937] [INSPIRE].
N. Kobayashi, T. Nishioka, Y. Sato and K. Watanabe, Towards a C-theorem in defect CFT, JHEP 01 (2019) 039 [arXiv:1810.06995] [INSPIRE].
S. Giombi et al., Chern-Simons Theory with Vector Fermion Matter, Eur. Phys. J. C 72 (2012) 2112 [arXiv:1110.4386] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, d = 3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories, JHEP 03 (2012) 037 [arXiv:1110.4382] [INSPIRE].
O. Aharony, G. Gur-Ari and R. Yacoby, Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions, JHEP 12 (2012) 028 [arXiv:1207.4593] [INSPIRE].
O. Aharony, Baryons, monopoles and dualities in Chern-Simons-matter theories, JHEP 02 (2016) 093 [arXiv:1512.00161] [INSPIRE].
P.-S. Hsin and N. Seiberg, Level/rank Duality and Chern-Simons-Matter Theories, JHEP 09 (2016) 095 [arXiv:1607.07457] [INSPIRE].
Y. Sato, Free energy and defect C-theorem in free fermion, JHEP 05 (2021) 202 [arXiv:2102.11468] [INSPIRE].
A. Allais, Double-trace deformations, holography and the c-conjecture, JHEP 11 (2010) 040 [arXiv:1007.2047] [INSPIRE].
J.N. Laia and D. Tong, Flowing Between Fermionic Fixed Points, JHEP 11 (2011) 131 [arXiv:1108.2216] [INSPIRE].
R. Camporesi and A. Higuchi, On the Eigen functions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [gr-qc/9505009] [INSPIRE].
A.A. Bytsenko, G. Cognola, L. Vanzo and S. Zerbini, Quantum fields and extended objects in space-times with constant curvature spatial section, Phys. Rept. 266 (1996) 1 [hep-th/9505061] [INSPIRE].
A.J. Amsel and D. Marolf, Supersymmetric Multi-trace Boundary Conditions in AdS, Class. Quant. Grav. 26 (2009) 025010 [arXiv:0808.2184] [INSPIRE].
C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [hep-th/9901021] [INSPIRE].
K. Jensen and A. O’Bannon, Constraint on Defect and Boundary Renormalization Group Flows, Phys. Rev. Lett. 116 (2016) 091601 [arXiv:1509.02160] [INSPIRE].
C. Herzog, K.-W. Huang and K. Jensen, Displacement Operators and Constraints on Boundary Central Charges, Phys. Rev. Lett. 120 (2018) 021601 [arXiv:1709.07431] [INSPIRE].
D.V. Fursaev and S.N. Solodukhin, Anomalies, entropy and boundaries, Phys. Rev. D 93 (2016) 084021 [arXiv:1601.06418] [INSPIRE].
J.S. Dowker, J.S. Apps, K. Kirsten and M. Bordag, Spectral invariants for the Dirac equation on the d ball with various boundary conditions, Class. Quant. Grav. 13 (1996) 2911 [hep-th/9511060] [INSPIRE].
D. Rodriguez-Gomez and J.G. Russo, Boundary Conformal Anomalies on Hyperbolic Spaces and Euclidean Balls, JHEP 12 (2017) 066 [arXiv:1710.09327] [INSPIRE].
J.A. Gracey, Calculation of exponent eta to O(1/N2) in the O(N) Gross-Neveu model, Int. J. Mod. Phys. A 6 (1991) 395 [Erratum ibid. 6 (1991) 2755] [INSPIRE].
J.A. Gracey, Anomalous mass dimension at O(1/N2) in the O(N) Gross-Neveu model, Phys. Lett. B 297 (1992) 293 [INSPIRE].
J.A. Gracey, Computation of β′(gc) at O(1/N2) in the O(N ) Gross-Neveu model in arbitrary dimensions, Int. J. Mod. Phys. A 9 (1994) 567 [hep-th/9306106] [INSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [INSPIRE].
E. D’Hoker, D.Z. Freedman, S.D. Mathur, A. Matusis and L. Rastelli, Graviton exchange and complete four point functions in the AdS/CFT correspondence, Nucl. Phys. B 562 (1999) 353 [hep-th/9903196] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal four point functions and the operator product expansion, Nucl. Phys. B 599 (2001) 459 [hep-th/0011040] [INSPIRE].
S. Giombi, R. Roiban and A.A. Tseytlin, Half-BPS Wilson loop and AdS2/CFT1, Nucl. Phys. B 922 (2017) 499 [arXiv:1706.00756] [INSPIRE].
M. Beccaria, S. Giombi and A.A. Tseytlin, Correlators on non-supersymmetric Wilson line in \( \mathcal{N} \) = 4 SYM and AdS2/CFT1, JHEP 05 (2019) 122 [arXiv:1903.04365] [INSPIRE].
S. Rychkov and Z.M. Tan, The ϵ-expansion from conformal field theory, J. Phys. A 48 (2015) 29FT01 [arXiv:1505.00963] [INSPIRE].
S. Giombi, H. Khanchandani and X. Zhou, Aspects of CFTs on Real Projective Space, J. Phys. A 54 (2021) 024003 [arXiv:2009.03290] [INSPIRE].
L. Slater, Generalised Hypergeometric Functions, Cambridge University Press, Cambridge, U.K. (1966) [DOI].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2110.04268
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Giombi, S., Helfenberger, E. & Khanchandani, H. Fermions in AdS and Gross-Neveu BCFT. J. High Energ. Phys. 2022, 18 (2022). https://doi.org/10.1007/JHEP07(2022)018
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2022)018