The constraints of conformal symmetry on RG flows

By Z. Komargodski. 2011

285 citations recorded by the source corpus.

A bstractIf the coupling constants in QFT are promoted to functions of space-time, the dependence of the path integral on these couplings is highly constrained by conformal symmetry. We begin the present note by showing that this idea leads to a new proof of Zamolodchikov’s theorem. We then review how this simple observation also leads to a derivation of the a-theorem. We exemplify the general procedure in some interacting theories in four space-time dimensions. We concentrate on Banks-Zaks and weakly relevant flows, which can be controlled by ordinary and conformal perturbation theories, respectively. We compute explicitly the dependence of the path integral on the coupling constants and extract the change in the a-anomaly (this agrees with more conventional computations of the same quantity). We also discuss some general properties of the sum rule found in [1] and study it in several examples.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a253f87deed365327ee509ba37bc0174ce0436ad

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Citations in the corpus

Interpolating between a and F (2014, background): “A general proof of the a-theorem has become available relatively recently [8, 9].”
Sphere partition functions and the Zamolodchikov metric (2014, background): “This is necessary for its interpretation as a monotonic function under renormalization group flows [1,4,5,6,7].”
The Casimir energy in curved space and its supersymmetric counterpart (2015, background): “In particular, Cardy conjectured [3] that there exists a decreasing function along RG flows, reducing to a at the fixed points [4, 5, 6].”
Mutual information and the F-theorem (2015, background): “a-theorem in four dimensions [3, 4] — see also [5].”
Beyond the Cosmological Standard Model (2014, unknown): “For example, in the theory of a dilaton we have A2→2 1−loop ∼ ∣A2→2 tree ∣∣2 ∼ ( s(2) + t(2) + u(2) )2 ∼ O(s(4)) , so the dispersion relation holds at tree level [546, 1020].”
Convexity and liberation at large spin (2012, methodology): “Simple examples based on an application of the optical theorem are discussed in [14,15,16,17].”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “In two and four dimensions, it was shown [1-4] that every unitary renormalization group (RG) flow connecting a CFTUV at short distances to a CFTIR at long distances must respect the inequality”
Comments on holographic entanglement entropy and RG flows (2012, background): “Recently, a remarkable new proof of this c-theorem was presented for any four-dimensional RG flow connecting two conformal fixed points [12].”
Limit cycles and conformal invariance (2012, background): “(2.1) Alternatively, Komargodski [15] argues that the functional is made invariant under Weyl transformations by adding a conformal compensator τ(x).”