arXiv subjects

Silviu S. Pufu

Publications and source records attributed to Silviu S. Pufu.

At least 73 records · Page 4Linked to original sources

arXiv2015

Three-sphere free energy for classical gauge groups

In this note, we calculate the $S^3$ free energy $F$ of 3-d ${\cal N}\geq 4$ supersymmetric gauge theories with $U(N)$, $O(N)$, and $USp(2N)$ gauge groups and matter hypermultiplets in the fundamental and two-index tensor representations. Supersymmetric localization reduces the computation of $F$ to a matrix model that we solve in the large $N$ limit using two different methods. The first method is a saddle point approximation first introduced in arXiv:1011.5487, which we extend to next-to-leading order in $1/N$. The second method generalizes the Fermi gas approach of arXiv:1110.4066 to theories with symplectic and orthogonal gauge groups, and yields an expression for $F$ valid to all orders in $1/N$. In developing the second method, we use a non-trivial generalization of the Cauchy determinant formula.

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arXiv2015

Bootstrapping $O(N)$ Vector Models with Four Supercharges in $3 \leq d \leq4$

We analyze the conformal bootstrap constraints in theories with four supercharges and a global $O(N) \times U(1)$ flavor symmetry in $3 \leq d \leq 4$ dimensions. In particular, we consider the 4-point function of $O(N)$-fundamental chiral operators $Z_i$ that have no chiral primary in the $O(N)$-singlet sector of their OPE. We find features in our numerical bounds that nearly coincide with the theory of $N+1$ chiral super-fields with superpotential $W = X \sum_{i=1}^N Z_i^2$, as well as general bounds on SCFTs where $\sum_{i=1}^N Z_i^2$ vanishes in the chiral ring.

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arXiv2015

Accidental Symmetries and the Conformal Bootstrap

We study an ${\cal N} = 2$ supersymmetric generalization of the three-dimensional critical $O(N)$ vector model that is described by $N+1$ chiral superfields with superpotential $W = g_1 X \sum_i Z_i^2 + g_2 X^3$. By combining the tools of the conformal bootstrap with results obtained through supersymmetric localization, we argue that this model exhibits a symmetry enhancement at the infrared superconformal fixed point due to $g_2$ flowing to zero. This example is special in that the existence of an infrared fixed point with $g_1,g_2\neq 0$, which does not exhibit symmetry enhancement, does not generally lead to any obvious unitarity violations or other inconsistencies. We do show, however, that the $F$-theorem excludes the models with $g_1,g_2\neq 0$ for $N>5$. The conformal bootstrap provides a stronger constraint and excludes such models for $N>2$. We provide evidence that the $g_2=0$ models, which have the enhanced $O(N)\times U(1)$ symmetry, come close to saturating the bootstrap bounds. We extend our analysis to fractional dimensions where we can motivate the nonexistence of the $g_1,g_2\neq 0$ models by studying them perturbatively in the $4-ε$ expansion.

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arXiv2015

Bootstrapping $O(N)$ Vector Models in $4<d<6$

We use the conformal bootstrap to study conformal field theories with $O(N)$ global symmetry in $d=5$ and $d=5.95$ spacetime dimensions that have a scalar operator $ϕ_i$ transforming as an $O(N)$ vector. The crossing symmetry of the four-point function of this $O(N)$ vector operator, along with unitarity assumptions, determine constraints on the scaling dimensions of conformal primary operators in the $ϕ_i \times ϕ_j$ OPE. Imposing a lower bound on the second smallest scaling dimension of such an $O(N)$-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting $O(N)$-symmetric CFT conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest $O(N)$ singlet in the $ϕ_i \times ϕ_j$ OPE, we observe that this kink disappears in $d =5$ for small enough $N$, suggesting that in this case an interacting $O(N)$ CFT may cease to exist for $N$ below a certain critical value.

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arXiv2014

Exact Correlators of BPS Operators from the 3d Superconformal Bootstrap

We use the superconformal bootstrap to derive exact relations between OPE coefficients in three-dimensional superconformal field theories with ${\cal N} \geq 4$ supersymmetry. These relations follow from a consistent truncation of the crossing symmetry equations that is associated with the cohomology of a certain supercharge. In ${\cal N} = 4$ SCFTs, the non-trivial cohomology classes are in one-to-one correspondence with certain half-BPS operators, provided that these operators are restricted to lie on a line. The relations we find are powerful enough to allow us to determine an infinite number of OPE coefficients in the interacting SCFT ($U(2)_2 \times U(1)_{-2}$ ABJ theory) that constitutes the IR limit of $O(3)$ ${\cal N} = 8$ super-Yang-Mills theory. More generally, in ${\cal N} = 8$ SCFTs with a unique stress tensor, we are led to conjecture that many superconformal multiplets allowed by group theory must actually be absent from the spectrum, and we test this conjecture in known ${\cal N} = 8$ SCFTs using the superconformal index. For generic ${\cal N} = 8$ SCFTs, we also improve on numerical bootstrap bounds on OPE coefficients of short and semi-short multiplets and discuss their relation to the exact relations between OPE coefficients we derived. In particular, we show that the kink previously observed in these bounds arises from the disappearance of a certain quarter-BPS multiplet, and that the location of the kink is likely tied to the existence of the $U(2)_2 \times U(1)_{-2}$ ABJ theory, which can be argued to not possess this multiplet.

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arXiv2014

The ${\cal N} = 8$ Superconformal Bootstrap in Three Dimensions

We analyze the constraints imposed by unitarity and crossing symmetry on the four-point function of the stress-tensor multiplet of ${\cal N}=8$ 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 stress-tensor 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 stress-tensor central charge. To make contact with known ${\cal N}=8$ 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 $U(1)\times U(1)$ ABJM theory.

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arXiv2014

Exact results for five-dimensional superconformal field theories with gravity duals

We apply the technique of supersymmetric localization to exactly compute the $S^5$ partition function of several large $N$ superconformal field theories in five dimensions that have $AdS_6$ duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the $S^5$ free energy to a holographic computation of entanglement entropy in the $AdS_6$ duals and find perfect agreement. In particular, we reproduce the $N^{5/2}$ scaling of the $S^5$ free energy that was expected from supergravity.

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arXiv2014

The Holography of F-maximization

We find new supersymmetric backgrounds of ${\cal N} = 8$ gauged supergravity in four Euclidean dimensions that are dual to deformations of ABJM theory on $S^3$. The deformations encode the most general choice of $U(1)_R$ symmetry used to define the theory on $S^3$. We work within an ${\cal N} = 2$ truncation of the ${\cal N} = 8$ supergravity theory obtained via a group theory argument. We find perfect agreement between the $S^3$ free energy computed from our supergravity backgrounds and the previous field theory computations of the same quantity based on supersymmetric localization and matrix model techniques.

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arXiv2014

Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics

The space of local operators in three-dimensional quantum electrodynamics contains monopole operators that create $n$ units of gauge flux emanating from the insertion point. This paper uses the state-operator correspondence to calculate the anomalous dimensions of these monopole operators perturbatively to next-to-leading order in the $1/N_f$ expansion, thus improving on the existing leading order results in the literature. Here, $N_f$ is the number of two-component complex fermion flavors. The scaling dimension of the $n=1$ monopole operator is $0.265 N_f - 0.0383 + O(1/N_f)$ at the infrared conformal fixed point.

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arXiv2013

Holography for ${\cal N}=2^*$ on $S^4$

We find the gravity dual of $\mathcal{N}=2^*$ super-Yang-Mills theory on $S^4$ and use holography to calculate the universal contribution to the corresponding $S^4$ free energy at large $N$ and large 't Hooft coupling. Our result matches the expression previously computed using supersymmetric localization in the field theory. This match represents a non-trivial precision test of holography in a non-conformal, Euclidean signature setting.

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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

Monopole Taxonomy in Three-Dimensional Conformal Field Theories

We study monopole operators at the infrared fixed points of Abelian and non-Abelian gauge theories with N_f fermion flavors in three dimensions. At large N_f, independent monopole operators can be defined via the state-operator correspondence only for stable monopole backgrounds. In Abelian theories, every monopole background is stable. In the non-Abelian case, we find that many (but not all) backgrounds are stable in each topological class. We calculate the infrared scaling dimensions of the corresponding operators through next-to-leading order in 1/N_f. In the case of U(N_c) QCD with N_f fundamental fermions (and in particular in the QED case, N_c =1), we find that the monopole operators transform as non-trivial irreducible representations of the SU(N_f) flavor symmetry group.

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arXiv2013

Monopoles in 2+1-dimensional conformal field theories with global U(1) symmetry

In 2+1-dimensional conformal field theories with a global U(1) symmetry, monopoles can be introduced through a background gauge field that couples to the U(1) conserved current. We use the state-operator correspondence to calculate scaling dimensions of such monopoles. We obtain the next-to-leading term in the 1/N_b expansion of the Wilson-Fisher fixed point in the theory of N_b complex bosons.

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arXiv2012

Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?

The renormalized entanglement entropy (REE) across a circle of radius R has been proposed as a c-function in Poincaré invariant (2+1)-dimensional field theory. A proof has been presented of its monotonic behavior as a function of R, based on the strong subadditivity of entanglement entropy. However, this proof does not directly establish stationarity of REE at conformal fixed points of the renormalization group. In this note we study the REE for the free massive scalar field theory near the UV fixed point described by a massless scalar. Our numerical calculation indicates that the REE is not stationary at the UV fixed point.

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arXiv2012

On Shape Dependence and RG Flow of Entanglement Entropy

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface has a conical or a wedge singularity. In (2+1)-dimensional field theory with a mass gap we calculate, for an arbitrary smooth entanglement contour, the expansion of the entropy in inverse odd powers of the mass. We show that the shape-dependent coefficients that arise are even powers of the extrinsic curvature and its derivatives. A useful dual construction of a (2+1)-dimensional theory, which allows us to exhibit these properties, is provided by the CGLP background. This smooth warped throat solution of 11-dimensional supergravity describes renormalization group flow from a conformal field theory in the UV to a gapped one in the IR. For this flow we calculate the recently introduced renormalized entanglement entropy and confirm that it is a monotonic function.

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arXiv2012

Renyi Entropies for Free Field Theories

Renyi entropies S_q are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q>=0. For (d+1)-dimensional conformal field theories, the Renyi entropies across S^{d-1} may be extracted from the thermal partition functions of these theories on either (d+1)-dimensional de Sitter space or R x H^d, where H^d is the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d+1)-dimensional sphere and S^1 x H^d, respectively. We calculate the Renyi entropies of free massless scalars and fermions in d=2, and show how using zeta-function regularization one finds agreement between the calculations on the branched coverings of S^3 and on S^1 x H^2. Analogous calculations for massive free fields provide monotonic interpolating functions between the Renyi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Renyi entropy calculations in d>2.

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arXiv2012

Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N_F of bosonic and/or fermionic flavors to the first subleading order in 1/N_F. We also calculate the exact free energies of the analogous chiral and non-chiral {\cal N} = 2 supersymmetric theories using localization, and find agreement with the 1/N_F expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.

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arXiv2011

F-Theorem without Supersymmetry

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S^3 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 {\cal 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 Chern-Simons 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 S^d 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.

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