Results 11  20
of
57
PUPT2472 Interpolating between a and F
"... We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension d we define the quantity F ̃ = sin(pid/2) logZ, where Z is the path integral of the Euclidean CFT on the ddimensional round sphere. F ̃ smoothly interpolates between (−1)d/2pi/2 ti ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
We study the dimensional continuation of the sphere free energy in conformal field theories. In continuous dimension d we define the quantity F ̃ = sin(pid/2) logZ, where Z is the path integral of the Euclidean CFT on the ddimensional round sphere. F ̃ smoothly interpolates between (−1)d/2pi/2 times the aanomaly coefficient in even d, and (−1)(d+1)/2 times the sphere free energy F in odd d. We calculate F ̃ in various examples of unitary CFT that can be continued to noninteger dimensions, including free theories, doubletrace deformations at large N, and perturbative fixed points in the expansion. For all these examples F ̃ is positive, and it decreases under RG flow. Using perturbation theory in the coupling, we calculate F ̃ in the WilsonFisher fixed point of the O(N) vector model in d = 4 − to order 4. We use this result to estimate the value of F in the 3dimensional Ising model, and find that it is only a few percent below F of the free conformally coupled scalar field. We use similar methods to estimate the F values for the U(N) GrossNeveu model in d = 3 and the O(N) model in d = 5. Finally, we carry out the dimensional continuation of interacting theories with 4 supercharges, for which we suggest that F ̃ may be calculated exactly using an appropriate version of localization on Sd. Our approach provides an interpolation between the amaximization in d = 4 and the Fmaximization in d = 3. ar X iv
Phases of planar 5dimensional supersymmetric ChernSimons theory
"... In this paper we investigate the largeN behavior of 5dimensional N = 1 super YangMills with a level k ChernSimons term and an adjoint hypermultiplet. As in threedimensional ChernSimons theories, one must choose an integration contour to completely define the theory. Using localization, we red ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
In this paper we investigate the largeN behavior of 5dimensional N = 1 super YangMills with a level k ChernSimons term and an adjoint hypermultiplet. As in threedimensional ChernSimons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite YangMills coupling and for particular choices of the contours, we find that the freeenergy scales as N5/2 for U(N) gauge groups with large values of the ChernSimons ’t Hooft coupling, λ ̃ ≡ N/k. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the N5/2 behavior parallels other fixed points which have known supergravity duals. We also demonstrate that SU(N) gauge groups cannot have this N5/2 scaling for their freeenergy. At finite YangMills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang Mills phase to the ChernSimons phase. The phase transition exists for any value of λ̃, although the details differ between small and large values of λ̃. For pure ChernSimons theories we present evidence for a chain of phase transitions as λ ̃ is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the ChernSimons term leads to different physical properties for fundamental and antifundamental Wilson loops. Different choices of the integration contours also lead to different properties for the loops. ar
A Note on the Partition Function of ABJM theory on S3, Prog.Theor.Phys. 127 (2012) 229–242
 Exact Results on the ABJM Fermi Gas, JHEP 1210 (2012) 020, [arXiv:1207.4283], P. Putrov and M. Yamazaki, Exact ABJM Partition Function from TBA, Mod.Phys.Lett. A27 (2012) 1250200, [arXiv:1207.5066
, 2013
"... ar ..."
(Show Context)
HananyWitten effect and SL(2,Z) dualities in matrix models
, 2014
"... We provide tests of dualities for threedimensional N = 4 quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on S3. The dualities are generated by SL(2,Z) transformations and HananyWitten 5brane moves. These contain mirror symmetry as well as dua ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We provide tests of dualities for threedimensional N = 4 quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on S3. The dualities are generated by SL(2,Z) transformations and HananyWitten 5brane moves. These contain mirror symmetry as well as dualities identifiying fixed points of YangMills quivers and ChernSimons theories. The partition function is given by a matrix model, that can be nicely rearranged into a sequence of factors mimicking the brane realization. Identities obeyed by these elementary factors can be used to match the partition functions of dual theories, providing tests for the full web of dualities. In particular we are able to check mirror symmetry for linear and circular quivers with gauge nodes of arbitrary ranks. Our analysis also leads to a proof of a conjectured formula evaluating the matrix models of linear quiver SCFTs.
The N = 8 Superconformal Bootstrap in Three Dimensions
, 2014
"... We analyze the constraints imposed by unitarity and crossing symmetry on the fourpoint function of the stresstensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
We analyze the constraints imposed by unitarity and crossing symmetry on the fourpoint function of the stresstensor multiplet of N = 8 superconformal field theories in three dimensions. We first derive the superconformal blocks by analyzing the superconformal Ward identity. Our results imply that the OPE of the primary operator of the stresstensor multiplet with itself must have parity symmetry. We then analyze the relations between the crossing equations, and we find that these equations are mostly redundant. We implement the independent crossing constraints numerically and find bounds on OPE coefficients and operator dimensions as a function of the stresstensor central charge. To make contact with known N = 8 superconformal field theories, we compute this central charge in a few particular cases using supersymmetric localization. For limiting values of the central charge, our numerical bounds are nearly saturated by the large N limit of ABJM theory and also by the free U(1) × U(1) ABJM theory.
Article Reference Exact results in N = 8 $ $ \mathcal{N}=8 $ $ ChernSimonsmatter theories and quantum geometry
"... We show that, in ABJ(M) theories with N = 8 $ $ \mathcal{N}=8 $ $ supersymmetry, the nonperturbative sector of the partition function on the threesphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which ..."
Abstract
 Add to MetaCart
(Show Context)
We show that, in ABJ(M) theories with N = 8 $ $ \mathcal{N}=8 $ $ supersymmetry, the nonperturbative sector of the partition function on the threesphere simplifies drastically. Due to this simplification, we are able to write closed form expressions for the grand potential of these theories, which determines the full large N asymptotics. Moreover, we find explicit formulae for the generating functionals of their partition functions, for all values of the rank N of the gauge group: they involve Jacobi theta functions on the spectral curve associated to the planar limit. Exact quantization conditions for the spectral problem of the Fermi gas are then obtained from the vanishing of the theta function. We also show that the partition function, as a function of N, can be extended in a natural way to an entire function on the full complex plane, and we explore some possible consequences of this fact for the quantum geometry of Mtheory and for putative de Sitter extensions.
Disclaimer: layout of this document may differ from the published version.
"... The partition function on the threesphere of N = 3 ChernSimonsmatter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N = 2 supersymmetry, the partition function corresponds to a gas of interacting fermions in one dimension. The large N limit ..."
Abstract
 Add to MetaCart
(Show Context)
The partition function on the threesphere of N = 3 ChernSimonsmatter theories can be formulated in terms of an ideal Fermi gas. In this paper we show that, in theories with N = 2 supersymmetry, the partition function corresponds to a gas of interacting fermions in one dimension. The large N limit is the thermodynamic limit of the gas and it can be analyzed with the Hartree and ThomasFermi approximations, which lead to the known large N solutions of these models. We use this interacting fermion picture to analyze in detail N = 2 theories with one single node. In the case of theories with no longrange forces we incorporate exchange effects and argue that the partition function is given by an Airy function, as in N = 3 theories. For the theory with g adjoint superfields and longrange forces, the ThomasFermi approximation leads to an integral equation which determines the large N, strongly coupled Rcharge