Improved bounds for CFT’s with global symmetries

By A. Vichi. 2011

156 citations recorded by the source corpus.

A bstractThe four point functions of Conformal Field Theories (CFT’s) with global symmetries give rise to multiple crossing symmetry constraints. We explicitly study the correlator of four scalar operators transforming in the fundamental representation of a global SO(N) and the correlator of chiral and anti-chiral superfields in a superconformal field theory. In both cases the constraints take the form of a triple sum rule, whose feasibility can be translated into restrictions on the CFT spectrum and interactions. In the case of SO(N) global symmetry we derive bounds for the first scalar singlet operator entering the Operator Product Expansion (OPE) of two fundamental representations for different value of N. Bounds for the first scalar traceless-symmetric representation of the global symmetry are computed as well. Results for superconformal field theories improve previous investigations due to the use of the full set of constraints. Our analysis only assumes unitarity of the CFT, crossing symmetry of the four point function and existence of an OPE for scalars.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b5f16be4a13af717f516feaa355b3d0838b17622

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In Nuclear and High Energy Physics

Citations in the corpus

Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$c-Minimization and Precise Critical Exponents (2012, background): “here are always as many equations as representation channels and the total constraining power is expected to be comparable to the Z 2-symmetric case. In 4D, this has been convincingly demonstrated in [22,23], where many strong bounds for O(N) and SU(N) symmetric CFTs have been obtained. It would be ”
The bootstrap program for boundary CFTd (2012, background): “This approach has been refined and extended in a series of papers [5, 6, 7, 8, 9, 10, 11, 12, 13].”
Bootstrapping mixed correlators in the 3D Ising model (2014, background): “The conformal bootstrap [1, 2] in D > 2 dimensions has produced remarkable results, including numerical bounds on operator dimensions and OPE coefficients [3–29], analytical constraints [30–36], and recently a precise conjecture for the Z2-even spectrum of the 3D Ising model [23].”
Universality of long-distance AdS physics from the CFT bootstrap (2014, methodology): “The bootstrap was originally developed in the case of CFT2 [1, 2], and has recently seen extensive analytic [7, 9, 14, 40–43] and numerical [3, 7, 44–61] application in CFT≥3.”
Projectors, shadows, and conformal blocks (2012, background): “Computations of scalar superconformal blocks allowed for similar bounds in 4d superconformal theories [14, 17, 18].”
Carving out the space of 4D CFTs (2011, methodology): “Previously, lower bounds on the central charge in both general CFTs and SCFTs were explored in [52, 53, 55].”
Bootstrapping SCFTs with four supercharges (2015, unknown): “The results of the previous sections suggest that the structure of these “bootstrap equations” should be very similar to those that were studied in the case of d = 4, N = 1 SCFTs in [14, 26, 51, 56], and indeed this is what we find.”