arXiv subjects

Simone Giombi

Publications and source records attributed to Simone Giombi.

At least 73 records · Page 4Linked to original sources

arXiv2015

Critical $Sp(N)$ Models in $6-ε$ Dimensions and Higher Spin dS/CFT

Theories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field Theory correspondence. We consider an $Sp(N)$ invariant theory of $N$ anti-commuting scalars and one commuting scalar, which has cubic interactions and is renormalizable in 6 dimensions. For any even $N$ we find an IR stable fixed point in $6-ε$ dimensions at imaginary values of coupling constants. Using calculations up to three loop order, we develop $ε$ expansions for several operator dimensions and for the sphere free energy $F$. The conjectured $F$-theorem is obeyed in spite of the non-unitarity of the theory. The $1/N$ expansion in the $Sp(N)$ theory is related to that in the corresponding $O(N)$ symmetric theory by the change of sign of $N$. Our results point to the existence of interacting non-unitary 5-dimensional CFTs with $Sp(N)$ symmetry, where operator dimensions are real. We conjecture that these CFTs are dual to the minimal higher spin theory in 6-dimensional de Sitter space with Neumann future boundary conditions on the scalar field. For $N=2$ we show that the IR fixed point possesses an enhanced global symmetry given by the supergroup $OSp(1|2)$. This suggests the existence of $OSp(1|2)$ symmetric CFTs in dimensions smaller than 6. We show that the $6-ε$ expansions of the scaling dimensions and sphere free energy in our $OSp(1|2)$ model are the same as in the $q \rightarrow 0$ limit of the $q$-state Potts model.

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arXiv2015

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 $\tilde F=\sin (πd/2)\log Z$, where $Z$ is the path integral of the Euclidean CFT on the $d$-dimensional round sphere. $\tilde F$ smoothly interpolates between $(-1)^{d/2}π/2$ times the $a$-anomaly coefficient in even $d$, and $(-1)^{(d+1)/2}$ times the sphere free energy $F$ in odd $d$. We calculate $\tilde F$ in various examples of unitary CFT that can be continued to non-integer dimensions, including free theories, double-trace deformations at large $N$, and perturbative fixed points in the $ε$ expansion. For all these examples $\tilde F$ is positive, and it decreases under RG flow. Using perturbation theory in the coupling, we calculate $\tilde F$ in the Wilson-Fisher fixed point of the $O(N)$ vector model in $d=4-ε$ to order $ε^4$. We use this result to estimate the value of $F$ in the 3-dimensional 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 $U(N)$ Gross-Neveu 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 $\tilde F$ may be calculated exactly using an appropriate version of localization on $S^d$. Our approach provides an interpolation between the $a$-maximization in $d=4$ and the $F$-maximization in $d=3$.

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arXiv2014

Three Loop Analysis of the Critical $O(N)$ Models in $6-ε$ Dimensions

We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-ε$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 σ(ϕ^i)^2 + \frac{1}{6}g_2 σ^3$. We calculate the 3-loop beta functions for the two couplings and use them to determine certain operator scaling dimensions at the IR stable fixed point up to order $ε^3$. We also use the beta functions to determine the corrections to the critical value of $N$ below which there is no fixed point at real couplings. The result suggests a very significant reduction in the critical value as the dimension is decreased to $5$. We also study the theory with $N=1$, which has a $Z_2$ symmetry under $ϕ\rightarrow -ϕ$. We show that it possesses an IR stable fixed point at imaginary couplings which can be reached by flow from a nearby fixed point describing a pair of $N=0$ theories. We calculate certain operator scaling dimensions at the IR fixed point of the $N=1$ theory and suggest that, upon continuation to two dimensions, it describes a non-unitary conformal minimal model.

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arXiv2014

Partition Functions and Casimir Energies in Higher Spin AdS_{d+1}/CFT_d

Recently, the one-loop free energy of higher spin (HS) theories in Euclidean AdS_{d+1} was calculated and matched with the order N^0 term in the free energy of the large N "vectorial" scalar CFT on the S^d boundary. Here we extend this matching to the boundary theory defined on S^1 x S^{d-1}, where the length of S^1 may be interpreted as the inverse temperature. It has been shown that the large N limit of the partition function on S^1 x S^2 in the U(N) singlet sector of the CFT of N free complex scalars matches the one-loop thermal partition function of the Vasiliev theory in AdS_4, while in the O(N) singlet sector of the CFT of N real scalars it matches the minimal theory containing even spins only. We extend this matching to all dimensions d. We also calculate partition functions for the singlet sectors of free fermion CFT's in various dimensions and match them with appropriately defined higher spin theories, which for d>3 contain massless gauge fields with mixed symmetry. In the zero-temperature case R x S^{d-1} we calculate the Casimir energy in the scalar or fermionic CFT and match it with the one-loop correction in the global AdS_{d+1}. For any odd-dimensional CFT the Casimir energy must vanish on general grounds, and we show that the HS duals obey this. In the U(N) symmetric case, we exhibit the vanishing of the regularized 1-loop Casimir energy of the dual HS theory in AdS_{d+1}. In the minimal HS theory the vacuum energy vanishes for odd d while for even d it is equal to the Casimir energy of a single conformal scalar in R x S^{d-1} which is again consistent with AdS/CFT, provided the minimal HS coupling constant is ~ 1/(N-1). We demonstrate analogous results for singlet sectors of theories of N Dirac or Majorana fermions. We also discuss extensions to CFT's containing N_f flavors in the fundamental representation of U(N) or O(N).

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arXiv2014

Critical $O(N)$ Models in $6-ε$ Dimensions

We revisit the classic $O(N)$ symmetric scalar field theories in $d$ dimensions with interaction $(ϕ^i ϕ^i)^2$. For $2 1038$. We show that the $1/N$ expansions of various operator scaling dimensions match the known results for the critical $O(N)$ theory continued to $d=6-ε$. These results suggest that, for sufficiently large $N$, there are 5-dimensional unitary $O(N)$ symmetric interacting CFT's; they should be dual to the Vasiliev higher-spin theory in AdS$_6$ with alternate boundary conditions for the bulk scalar. Using these CFT's we provide a new test of the 5-dimensional $F$-theorem, and also find a new counterexample for the $C_T$ theorem.

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arXiv2014

Higher Spin AdS$_{d+1}$/CFT$_d$ at One Loop

Following arXiv:1308.2337, we carry out one loop tests of higher spin AdS$_{d+1}$/CFT$_d$ correspondences for $d\geq 2$. The Vasiliev theories in AdS$_{d+1}$, which contain each integer spin once, are related to the $U(N)$ singlet sector of the $d$-dimensional CFT of $N$ free complex scalar fields; the minimal theories containing each even spin once -- to the $O(N)$ singlet sector of the CFT of $N$ free real scalar fields. Using analytic continuation of higher spin zeta functions, which naturally regulate the spin sums, we calculate one loop vacuum energies in Euclidean AdS$_{d+1}$. In even $d$ we compare the result with the $O(N^0)$ correction to the $a$-coefficient of the Weyl anomaly; in odd $d$ -- with the $O(N^0)$ correction to the free energy $F$ on the $d$-dimensional sphere. For the theories of integer spins, the correction vanishes in agreement with the CFT of $N$ free complex scalars. For the minimal theories, the correction always equals the contribution of one real conformal scalar field in $d$ dimensions. As explained in arXiv:1308.2337, this result may agree with the $O(N)$ singlet sector of the theory of $N$ real scalar fields, provided the coupling constant in the higher spin theory is identified as $G_N\sim 1/(N-1)$. Our calculations in even $d$ are closely related to finding the regularized $a$-anomalies of conformal higher spin theories. In each even $d$ we identify two such theories with vanishing $a$-anomaly: a theory of all integer spins, and a theory of all even spins coupled to a complex conformal scalar. We also discuss an interacting UV fixed point in $d=5$ obtained from the free scalar theory via an irrelevant double-trace quartic interaction. This interacting large $N$ theory is dual to the Vasiliev theory in AdS$_6$ where the bulk scalar is quantized with the alternate boundary condition.

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arXiv2013

One Loop Tests of Higher Spin AdS/CFT

Vasiliev's type A higher spin theories in AdS4 have been conjectured to be dual to the U(N) or O(N) singlet sectors in 3-d conformal field theories with N-component scalar fields. We compare the O(N^0) correction to the 3-sphere free energy F in the CFTs with corresponding calculations in the higher spin theories. This requires evaluating a regularized sum over one loop vacuum energies of an infinite set of massless higher spin gauge fields in Euclidean AdS4. For the Vasiliev theory including fields of all integer spin and a scalar with Delta=1 boundary condition, we show that the regularized sum vanishes. This is in perfect agreement with the vanishing of subleading corrections to F in the U(N) singlet sector of the theory of N free complex scalar fields. For the minimal Vasiliev theory including fields of only even spin, the regularized sum remarkably equals the value of F for one free real scalar field. This result may agree with the O(N) singlet sector of the theory of N real scalar fields, provided the coupling constant in the Vasiliev theory is identified as G_N ~ 1/(N-1). Similarly, consideration of the USp(N) singlet sector for N complex scalar fields, which we conjecture to be dual to the husp(2;0|4) Vasiliev theory, requires G_N ~ 1/(N+1). We also test the higher spin AdS3/CFT2 conjectures by calculating the regularized sum over one loop vacuum energies of higher spin fields in AdS3. We match the result with the O(N^0) term in the central charge of the W_N minimal models; this requires a certain truncation of the CFT operator spectrum so that the bulk theory contains two real scalar fields with the same boundary conditions.

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arXiv2013

AdS Description of Induced Higher-Spin Gauge Theory

We study deformations of three-dimensional large N CFTs by double-trace operators constructed from spin s single-trace operators of dimension Δ. These theories possess UV fixed points, and we calculate the change of the 3-sphere free energy δF= F_{UV}- F_{IR}. To describe the UV fixed point using the dual AdS_4 space we modify the boundary conditions on the spin s field in the bulk; this approach produces δF in agreement with the field theory calculations. If the spin s operator is a conserved current, then the fixed point is described by an induced parity invariant conformal spin s gauge theory. The low spin examples are QED_3 (s=1) and the 3-d induced conformal gravity (s=2). When the original CFT is that of N conformal complex scalar or fermion fields, the U(N) singlet sector of the induced 3-d gauge theory is dual to Vasiliev's theory in AdS_4 with alternate boundary conditions on the spin s massless gauge field. We test this correspondence by calculating the leading term in δF for large N. We show that the coefficient of (1/2)\log N in δF is equal to the number of spin s-1 gauge parameters that act trivially on the spin s gauge field. We discuss generalizations of these results to 3-d gauge theories including Chern-Simons terms and to theories where s is half-integer. We also argue that the Weyl anomaly a-coefficients of conformal spin s theories in even dimensions d, such as that of the Weyl-squared gravity in d=4, can be efficiently calculated using massless spin s fields in AdS_{d+1} with alternate boundary conditions. Using this method we derive a simple formula for the Weyl anomaly a-coefficients of the d=4 Fradkin-Tseytlin conformal higher-spin gauge fields. Similarly, using alternate boundary conditions in AdS_3 we reproduce the well-known central charge c=-26 of the bc ghosts in 2-d gravity, as well as its higher-spin generalizations.

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arXiv2013

A Note on CFT Correlators in Three Dimensions

In this note we present a simple method of constructing general conformally invariant three point functions of operators of various spins in three dimensions. Upon further imposing current conservation conditions, we find new parity violating structures for the three point functions involving either the stress-energy tensor, spin one currents, or higher spin currents. We find that all parity preserving structures for conformally invariant three point functions of higher spin conserved currents can be realized by free fields, whereas there is at most one parity violating structure for three point functions for each set of spins, which is not realized by free fields.

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arXiv2013

The Thermal Free Energy in Large N Chern-Simons-Matter Theories

We compute the thermal free energy in large N U(N) Chern-Simons-matter theories with matter fields (scalars and/or fermions) in the fundamental representation, in the large temperature limit. We note that in these theories the eigenvalue distribution of the holonomy of the gauge field along the thermal circle does not localize even at very high temperatures, and this affects the computation significantly. We verify that our results are consistent with the conjectured dualities between Chern-Simons-matter theories with scalar fields and with fermion fields, as well as with the strong-weak coupling duality of the N=2 supersymmetric Chern-Simons-matter theory.

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arXiv2012

The Higher Spin/Vector Model Duality

This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.

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arXiv2012

Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS

We study correlation functions of Wilson loops and local operators in a subsector of N=4 SYM which preserves two supercharges. Localization arguments allow to map the problem to a calculation in bosonic two-dimensional Yang-Mills theory. In turn, this can be reduced to computing correlators in certain Gaussian multi-matrix models. We focus on the correlation function of a Wilson loop and two local operators, and solve the corresponding three-matrix model exactly in the planar limit. We compare the strong coupling behavior to string theory in AdS_5xS^5, finding precise agreement. We pay particular attention to the case in which the local operators have large R-charge J \sim sqrt{lambda} at strong coupling.

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arXiv2012

Chern-Simons Theory with Vector Fermion Matter

We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R^2 as a function of the 't Hooft coupling lambda=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |lambda|=1; the conformal theory does not exist for |lambda|>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W-infinity algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.

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arXiv2011

On Higher Spin Gauge Theory and the Critical O(N) Model

We show that the differences between correlators of the critical O(N) vector model in three dimensions and those of the free theory are precisely accounted for by the change of boundary condition on the bulk scalar of the dual higher spin gauge theory in AdS4. Thus, the conjectured duality between Vasiliev's theory and the critical O(N) model follows, order by order in 1/N, from the duality with free field theory on the boundary.

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arXiv2011

Higher Spins in AdS and Twistorial Holography

In this paper we simplify and extend previous work on three-point functions in Vasiliev's higher spin gauge theory in AdS4. We work in a gauge in which the space-time dependence of Vasiliev's master fields is gauged away completely, leaving only the internal twistor-like variables. The correlation functions of boundary operators can be easily computed in this gauge. We find complete agreement of the tree level three point functions of higher spin currents in Vasiliev's theory with the conjectured dual free O(N) vector theory.

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arXiv2010

Higher Spin Gauge Theory and Holography: The Three-Point Functions

In this paper we calculate the tree level three-point functions of Vasiliev's higher spin gauge theory in AdS4 and find agreement with the correlators of the free field theory of N massless scalars in three dimensions in the O(N) singlet sector. This provides substantial evidence that Vasiliev theory is dual to the free field theory, thus verifying a conjecture of Klebanov and Polyakov. We also find agreement with the critical O(N) vector model, when the bulk scalar field is subject to the alternative boundary condition such that its dual operator has classical dimension 2.

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arXiv2009

The 1/2 BPS 't Hooft loops in N=4 SYM as instantons in 2d Yang-Mills

We extend the recent conjecture on the relation between a certain 1/8 BPS subsector of 4d N=4 SYM on S^2 and 2d Yang-Mills theory by turning on circular 1/2 BPS 't Hooft operators linked with S^2. We show that localization predicts that these 't Hooft operators and their correlation functions with Wilson operators on S^2 are captured by instanton contributions to the partition function of the 2d Yang-Mills theory. Based on this prediction, we compute explicitly correlation functions involving the 't Hooft operator, and observe precise agreement with S-duality predictions.

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arXiv2009

Notes on supersymmetric Wilson loops on a two-sphere

We study a recently discovered family of 1/8-BPS supersymmetric Wilson loops in N=4 super Yang-Mills theory and their string theory duals. The operators are defined for arbitrary contours on a two-sphere in space-time, and they were conjectured to be captured perturbatively by 2d bosonic Yang-Mills theory. In the AdS dual, they are described by pseudo-holomorphic string surfaces living on a certain submanifold of AdS_5 x S^5. We show that the regularized area of these string surfaces is invariant under area preserving diffeomorphisms of the boundary loop, in agreement with the conjecture. Further, we find a connection between the pseudo-holomorphicity equations and an auxiliary sigma-model on S^3, which may help to construct new 1/8-BPS string solutions. We also show that the conjectured relation to 2d Yang-Mills implies that a connected correlator of two Wilson loops is computed by a Hermitian Gaussian two-matrix model. On the AdS dual side, we argue that the connected correlator is described by two disconnected disks interacting through the exchange of supergravity modes, and we show that this agrees with the strong coupling planar limit of the two-matrix model.

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