From necklace quivers to the F -theorem, operator counting, and T (U(N))

Gulotta, Daniel R.; Herzog, Christopher P.; Pufu, Silviu S.

doi:10.1007/jhep12(2011)077

Cited by 76 publications

(98 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This analysis does not imply that F is decreased under relevant deformations which change the geometry away from AdS 4 . The scalar field φ and the change in the warp factor a do not decrease monotonically along the flow but this does not in itself contradict the arguments of [9]. From a top-down perspective scalar fields in four-dimensional gauged supergravity theories arise not just from breathing modes of the compact manifold, but also from the four-form flux in eleven dimensions.…”

Section: Discussionmentioning

confidence: 75%

“…Arguments for stationarity are based on the fact that F is extremized with respect to the R charges of an IR CFT [6] and (holographically) with respect to the parameters of the Sasaki-Einstein manifold Y 7 [3,7,8]. For monotonic decrease, it was shown in Klebanov et al [4] that the free energy decreases monotonically along weakly relevant flows, while [9] argued that the volume of the compact manifold should increase monotonically along an RG flow in holographic examples, implying monotonic decrease of F. In Freedman and Pufu [10] it was shown that F decreases along certain supersymmetric RG flows of deformations of the ABJM theory.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Holographic F Theorem

Taylor

Woodhead

2017

Front. Phys.

View full text Add to dashboard Cite

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension 3/2 < < 5/2. Therefore, the strongest version of the F theorem is in general violated.

show abstract

Section: Discussionmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

The Holographic F Theorem

Taylor

Woodhead

2017

Front. Phys.

View full text Add to dashboard Cite

show abstract

“…In particular, an independent formulation of the three-dimensional c-theorem was proposed in [22], where the c-function was identified at conformal fixed points with the constant term in the free energy evaluated on a three-sphere. A great deal of evidence for this F -theorem was gathered from a wide variety of field theory examples, e.g., [23][24][25][26][27][28][29]. 1 However, it was also known that the F -theorem coincides with the previous proposal using entanglement entropy [13].…”

Section: Jhep10(2015)003mentioning

confidence: 75%

“…However, we do not really need to make this assumption here or in the following discussion. Rather it is a notational convenience to introduce S(A s ) rather than using 28 Again, we note thatt1 ·t2 = 1 follows from the latter. Hence this inner product carries no information about the 'angle' at the null cusp.…”

Section: Jhep10(2015)003mentioning

confidence: 99%

Mutual information and the F-theorem

Casini

Huerta

Myers

et al. 2015

J. High Energ. Phys.

144

184

View full text Add to dashboard Cite

Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription for the monotonous quantity in the c-theorem for d = 3. This is in principle computable using any regularization for the entropy, and in particular is a definition suitable for lattice models. We rederive the proof of the c-theorem for d = 3 in terms of mutual information, and check our arguments with holographic entanglement entropy, a free scalar field, and an extensive mutual information model.

show abstract

“…earlier works [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. Especially it is worthwhile to mention that, according to [15] the expression of the coefficient C was given a geometrical interpretation as the classical volume inside the Fermi surface.…”

Section: Jhep11(2014)164mentioning

confidence: 99%

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

Moriyama

Nosaka

2014

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:We study the partition function of three-dimensional N = 4 superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as Z(N ) = e A C −1/3 Ai[C −1/3 (N − B)] with coefficients C, B and A and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of B for general N = 4 theories, a conjectural form of A for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.

show abstract

From necklace quivers to the F -theorem, operator counting, and T (U(N))

Cited by 76 publications

References 34 publications

The Holographic F Theorem

The Holographic F Theorem

Mutual information and the F-theorem

Partition functions of superconformal Chern-Simons theories from Fermi gas approach

Contact Info

Product

Resources

About