On renormalization group flows in four dimensions

By Z. Komargodski, A. Schwimmer. 2011

867 citations recorded by the source corpus.

A bstractWe discuss some general aspects of renormalization group flows in four dimensions. Every such flow can be reinterpreted in terms of a spontaneously broken conformal symmetry. We analyze in detail the consequences of trace anomalies for the effective action of the Nambu-Goldstone boson of broken conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly is “non-Abelian”, and leads to a positive-definite universal contribution to the S-matrix element of 2 → 2 dilaton scattering. Unitarity of the S-matrix results in a monotonically decreasing function that interpolates between the Euler anomalies in the ultraviolet and the infrared, thereby establishing the a-theorem.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9e149cfc078998c9d708dee1c5c4d3f4bc8557fe

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Citations in the corpus

Mutual information and the F-theorem (2015, background): “a-theorem in four dimensions [3, 4] — see also [5].”
Positive moments for scattering amplitudes (2020, background): “[11] Zohar Komargodski and Adam Schwimmer, “On Renormalization Group Flows in Four Dimensions,” JHEP 12, 099 (2011), arXiv:1107.”
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 constraints of conformal symmetry on RG flows (2011, methodology): “The following presentation of the proof of the a-theorem is completely equivalent to the one in [1].”
Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, background): “In d = 2 and d = 4, that central charge is strictly non-increasing along an RG flow from the UV to the IR [10, 11].”
The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, background): “gives a measure of the degrees of freedom of the theory and serves as a height function in theory space: for two CFTs connected by RG flow, aUV > aIR [24, 25].”
On the RG running of the entanglement entropy of a circle (2012, methodology): “The result of this paper for the monotonous RG running of the constant term of the circle entropy gives a QFT proof of the recent holographic result for this same quantity and the related ones for the free energy on a three sphere.”
Central charges for BCFTs and holography (2012, positive): “By comparing with the c-theorems in higher dimensions [32, 33, 34], we can conjecture (−1) d+1 2 rB d logZBCFTd drB ≤ 0.”
From correlation functions to event shapes (2013, neutral): “[15–17].”
Softness and amplitudes’ positivity for spinning particles (2016, background): “from the a-theorem [3] to the theory of pions [4–6], from WW-scattering [1, 7, 8] to composite Higgs models [8–11], from quantum gravity [12] to inflation [13, 14], from Galileons [15] to massive gravity [16], from the weak gravity conjecture [17, 18] to the OPE coefficients [19], from the conformal”
The effective theory of long strings (2013, result): “Let us now compare the situation we are finding here with the spontaneous breaking of conformal symmetry [57,58].”
Boundary conformal field theory and a boundary central charge (2017, background): “In two [7] and four [8] dimensions, the conjecture is in fact proven, providing a primitive tool to map out the space of quantum field theories.”
Interpolating between a and F (2014, background): “A general proof of the a-theorem has become available relatively recently [8, 9].”
The a-theorem and the asymptotics of 4D quantum field theory (2012, methodology): “The main tool in establishing these results is a generalization of the recent proof of the a-theorem by Komargodski and Schwimmer (KS) [1, 2].”