Interface conformal anomalies
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Springer
Received: May Revised: September Accepted: September Published: October
12, 17, 20, 21,
2020 2020 2020 2020
Christopher P. Herzog,a Kuo-Wei Huangb and Dmitri V. Vassilevichc,d a
Department of Mathematics, King’s College London, The Strand, London WC2R 2LS, U.K. b Department of Physics, Boston University, Commonwealth Avenue, Boston, MA 02215, U.S.A. c CMCC, Universidade Federal do ABC, Avenida dos Estados 5001, CEP 09210-580, Santo Andr´e, S.P., Brazil d Physics Department, Tomsk State University, 36 Lenin Ave., Tomsk, Russia
E-mail: [email protected], [email protected], [email protected] Abstract: We consider two d ≥ 2 conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we compute the heat kernel coefficients and interface central charges in free theories. The results are consistent with the known boundary CFT data via the folding trick. In d = 4, two interface invariants generally allowed as anomalies turn out to have vanishing interface charges. These missing invariants are constructed from components with odd parity with respect to flipping the orientation of the defect. We conjecture that all invariants constructed from components with odd parity may have vanishing coefficient for symmetric interfaces, even in the case of interacting interface CFT. Keywords: Boundary Quantum Field Theory, Conformal Field Theory, Field Theories in Higher Dimensions ArXiv ePrint: 2005.01689
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)132
JHEP10(2020)132
Interface conformal anomalies
Contents 1
2 Interface setup 2.1 Scalars 2.2 Spinors 2.3 U(1) gauge field
3 4 4 5
3 Heat kernel coefficients and central charges 3.1 Interface trace anomaly for d = 4 ICFTs
5 8
4 Concluding remarks
1
10
Introduction: why interfaces?
We study boundaries and defects in conformal field theory (CFT) because they have broad applications and because they are fundamental to our understanding of CFT and quantum field theory more generally. Boundaries and defects are generally present in most experimental realizations of critical systems, and they bring with them the potential for a wide variety of experimentally verifiable consequences, for example surface critical exponents. Beyond that, however, there are fundamental questions about the classification and “space” of quantum field theories that can be answered through a careful study of defects. While it is often stated that a conformal field theory is defined — through operator product expansion — by its local operator spectrum and set of three-point correlation functions, in fact there are often extended operators, such as Wilson lines, which must be included for a proper definition of the CFT (see e.g. [1]). These extended operators carry with them an additional defect interpretation. The complete classification of conformal defects or, equivalently, universality classes
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