Abstract
Recently it is found that, due to Weyl anomaly, a background scalar field induces a non-trivial Fermi condensation for theories with Yukawa couplings. For simplicity, the paper consider only scalar type Yukawa coupling and, in the BCFT case, only for a specific boundary condition. In these cases, the Weyl anomaly takes on a simple special form. In this paper, we generalize the results to more general situations. First, we obtain general expressions of Weyl anomaly due to a background scalar and pseudo scalar field in general 4d BCFTs. Then, we derive the general form of Fermi condensation from the Weyl anomaly. It is remarkable that, in general, Fermi condensation is non-zero even if there was not a non-vanishing scalar field background. Finally, we verify our results with free BCFT with Yukawa coupling to scalar and pseudo-scalar background potential with general chiral bag boundary condition and with holographic BCFT. In particular, we obtain the shape and curvature dependence of the Fermi condensate from the holographic one point function.
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C.A. Regal, M. Greiner and D.S. Jin, Observation of Resonance Condensation of Fermionic Atom Pairs, Phys. Rev. Lett. 92 (2004) 040403 [cond-mat/0401554] [INSPIRE].
C.-S. Chu and R.-X. Miao, Fermi Condensation induced by Weyl Anomaly, Phys. Rev. D 102 (2020) 046011 [arXiv:2004.05780] [INSPIRE].
L.E. Parker and D. Toms, Quantum Field Theory in Curved Spacetime: Quantized Field and Gravity, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2009), [DOI] [INSPIRE].
S.M. Carroll, Spacetime and Geometry, Cambridge University Press, (2019), [DOI].
R.-X. Miao and C.-S. Chu, Universality for Shape Dependence of Casimir Effects from Weyl Anomaly, JHEP 03 (2018) 046 [arXiv:1706.09652] [INSPIRE].
M.N. Chernodub, Anomalous Transport Due to the Conformal Anomaly, Phys. Rev. Lett. 117 (2016) 141601 [arXiv:1603.07993] [INSPIRE].
M.N. Chernodub, A. Cortijo and M.A.H. Vozmediano, Generation of a Nernst Current from the Conformal Anomaly in Dirac and Weyl Semimetals, Phys. Rev. Lett. 120 (2018) 206601 [arXiv:1712.05386] [INSPIRE].
C.-S. Chu and R.-X. Miao, Weyl Anomaly Induced Current in Boundary Quantum Field Theories, Phys. Rev. Lett. 121 (2018) 251602 [arXiv:1803.03068] [INSPIRE].
A. Chodos, R.L. Jaffe, K. Johnson, C.B. Thorn and V.F. Weisskopf, A New Extended Model of Hadrons, Phys. Rev. D 9 (1974) 3471 [INSPIRE].
A. Chodos, R.L. Jaffe, K. Johnson and C.B. Thorn, Baryon Structure in the Bag Theory, Phys. Rev. D 10 (1974) 2599 [INSPIRE].
D.V. Vassilevich, Heat kernel expansion: User’s manual, Phys. Rept. 388 (2003) 279 [hep-th/0306138] [INSPIRE].
P.-J. Hu, Q.-L. Hu and R.-X. Miao, Note on anomalous currents for a free theory, Phys. Rev. D 101 (2020) 125010 [arXiv:2004.06924] [INSPIRE].
J.L. Cardy, Boundary conformal field theory, hep-th/0411189 [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].
M.J. Duff, Twenty years of the Weyl anomaly, Class. Quant. Grav. 11 (1994) 1387 [hep-th/9308075] [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
D. Deutsch and P. Candelas, Boundary Effects in Quantum Field Theory, Phys. Rev. D 20 (1979) 3063 [INSPIRE].
D.M. McAvity and H. Osborn, A DeWitt expansion of the heat kernel for manifolds with a boundary, Class. Quant. Grav. 8 (1991) 603 [INSPIRE].
A. Petkou and K. Skenderis, A nonrenormalization theorem for conformal anomalies, Nucl. Phys. B 561 (1999) 100 [hep-th/9906030] [INSPIRE].
Z. Komargodski and A. Schwimmer, On Renormalization Group Flows in Four Dimensions, JHEP 12 (2011) 099 [arXiv:1107.3987] [INSPIRE].
H. Elvang, D.Z. Freedman, L.-Y. Hung, M. Kiermaier, R.C. Myers and S. Theisen, On renormalization group flows and the a-theorem in 6d, JHEP 10 (2012) 011 [arXiv:1205.3994] [INSPIRE].
C.P. Herzog, K.-W. Huang and K. Jensen, Universal Entanglement and Boundary Geometry in Conformal Field Theory, JHEP 01 (2016) 162 [arXiv:1510.00021] [INSPIRE].
A. Cappelli and A. Coste, On the Stress Tensor of Conformal Field Theories in Higher Dimensions, Nucl. Phys. B 314 (1989) 707 [INSPIRE].
A. Schwimmer and S. Theisen, Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching, Nucl. Phys. B 847 (2011) 590 [arXiv:1011.0696] [INSPIRE].
T. Takayanagi, Holographic Dual of BCFT, Phys. Rev. Lett. 107 (2011) 101602 [arXiv:1105.5165] [INSPIRE].
R.-X. Miao, C.-S. Chu and W.-Z. Guo, New proposal for a holographic boundary conformal field theory, Phys. Rev. D 96 (2017) 046005 [arXiv:1701.04275] [INSPIRE].
C.-S. Chu, R.-X. Miao and W.-Z. Guo, On New Proposal for Holographic BCFT, JHEP 04 (2017) 089 [arXiv:1701.07202] [INSPIRE].
R.-X. Miao, Holographic BCFT with Dirichlet Boundary Condition, JHEP 02 (2019) 025 [arXiv:1806.10777] [INSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
C.-S. Chu and R.-X. Miao, Anomalous Transport in Holographic Boundary Conformal Field Theories, JHEP 07 (2018) 005 [arXiv:1804.01648] [INSPIRE].
A. Faraji Astaneh and S.N. Solodukhin, Holographic calculation of boundary terms in conformal anomaly, Phys. Lett. B 769 (2017) 25 [arXiv:1702.00566] [INSPIRE].
R.-X. Miao, Casimir Effect, Weyl Anomaly and Displacement Operator in Boundary Conformal Field Theory, JHEP 07 (2019) 098 [arXiv:1808.05783] [INSPIRE].
M. Alishahiha and R. Fareghbal, Boundary CFT from Holography, Phys. Rev. D 84 (2011) 106002 [arXiv:1108.5607] [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
X. Dong, Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories, Phys. Rev. Lett. 116 (2016) 251602 [arXiv:1602.08493] [INSPIRE].
C. Imbimbo, A. Schwimmer, S. Theisen and S. Yankielowicz, Diffeomorphisms and holographic anomalies, Class. Quant. Grav. 17 (2000) 1129 [hep-th/9910267] [INSPIRE].
J.-J. Zheng, D. Li, Y.-Q. Zeng and R.-X. Miao, Anomalous Current Due to Weyl Anomaly for Conformal Field Theory, Phys. Lett. B 797 (2019) 134844 [arXiv:1904.07017] [INSPIRE].
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ArXiv ePrint: 2005.12975
All the Institutes of authors contribute equally to this work, the order of Institutes is adjusted for the assessment policy of SYSU (Chong-Sun Chu).
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Chu, CS., Miao, RX. Weyl anomaly induced Fermi condensation and holography. J. High Energ. Phys. 2020, 134 (2020). https://doi.org/10.1007/JHEP08(2020)134
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DOI: https://doi.org/10.1007/JHEP08(2020)134