F-theorem without supersymmetry

By I. Klebanov, Silviu S. Pufu, B. Safdi. 2011

364 citations recorded by the source corpus.

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with $ \mathcal{N} = 2 $ supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some non-Abelian gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on Sd and provide evidence that (−1)(d−1)/2 log|Z| decreases along RG flow; in the particular case d = 1 this is the well-known g-theorem.

Subfields: Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9ad067638b37b80352a1a0d97a09eb12beff140c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. S. Giombi
2. Z. Komargodski
3. I. Klebanov
4. T. Takayanagi
5. Silviu S. Pufu
6. Cyril Closset
7. Xi Yin
8. O. Aharony

In Nuclear and High Energy Physics

1. T. Takayanagi
2. R. Myers
3. T. Nishioka
4. S. Giombi
5. I. Klebanov
6. Z. Komargodski
7. O. Aharony
8. N. Seiberg

Citations in the corpus

• Exact results for five-dimensional superconformal field theories with gravity duals (2012, result): “It is also consistent with the observation that −F decreases under slightly relevant perturbations of a CFT, and that it remains constant under exactly marginal deformations [36].”
• On renormalization group flows and the a-theorem in 6d (2012, background): “For odd d, it was shown that this effective charge could also be identified by evaluating the partition function on a d-dimensional sphere [33] and so the conjecture is connected to the newly proposed F -theorem [34, 35].”
• Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions (2012, background): “Similarly, it would be interesting if (as in supersymmetric theories [61]) one could find a way to compute exactly the free energy of our theories on a Euclidean S(3) (at least in the large N limit), as this could provide another useful test of the duality; this free energy for our theories at weak ”
• Comments on holographic entanglement entropy and RG flows (2012, methodology): “Hence the exciting new field theoretic results of [36–39] provide further evidence for the same c-theorem in odd dimensions.”
• Cardy formulae for SUSY theories in d = 4 and d = 6 (2014, background): “Following [63] we regularize the sum by shifting m(2)B,n → M(2) B,n = m(2)B,n+μ 2 and m(2)F,n →M2 F,n = m(2)F,n+μ(2) and taking a derivative with respect to μ(2).”
• Mutual information and the F-theorem (2015, background): “Comparing this result with the exact value [23, 60],”
• Central charges for BCFTs and holography (2012, methodology): “Using the results in [30], we finally obtain its perturbative expansion w.”
• Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “(The eigenvalues of the relevant differential operators on S(3) can be found in [15].”
• Interpolating between a and F (2014, methodology): “This inequality was checked to be true in d = 3 [12, 70], where δF̃∆=2 = + ζ(3) 8π2 .”
• AdS description of induced higher-spin gauge theory (2013, methodology): “Note that for spin 1/2 this agrees with the result in [11,92].”
• The higher spin/vector model duality (2012, background): “This should also be relevant to explain the fact that the free energy of the Chern-Simons vector model on S(3) is expected to contain a term proportional to N(2) [61], essentially coming from the pure ChernSimons contribution, while the bulk coupling constant in Vasiliev’s theory should scale as g−2”
• One loop tests of higher spin AdS/CFT (2013, methodology): “Remarkably, this is exactly the same as the contribution to F of a single real conformal scalar field [25]! On the other hand, in the theory of N real free fields, the O(N) correction to F of course must vanish.”
• Entanglement entropy: Holography and renormalization group (2018, background): “They certainly deserve further investigations regardless of their applications to proving the conjectures for the higher-dimensional C-theorem (Giombi and Klebanov, 2015; Klebanov et al., 2011; Myers and Sinha, 2010, 2011).”
• The constraints of conformal symmetry on RG flows (2011, methodology): “Keeping only the significant terms in the weak coupling expansion, [32] found”