arXiv subjects

Nikolay Bobev

Publications and source records attributed to Nikolay Bobev.

At least 73 records · Page 4Linked to original sources

arXiv2017

Universal RG Flows Across Dimensions and Holography

We study RG flows between superconformal field theories living in different spacetime dimensions which exhibit universal properties, independent of the details of the UV and IR theories. In particular, when the UV and IR theories are both even-dimensional we establish exact universal relations between their conformal anomaly coefficients. We also provide strong evidence for similar relations between appropriately defined free energies for RG flows between odd-dimensional theories in the large $N$ limit. Holographically, these RG flows across dimensions are described by asymptotically AdS black branes in a gauged supergravity theory, which we exhibit explicitly. We also discuss the uplift of these solutions to string and M-theory and comment on how the entropy of such black branes is captured by the dual field theory.

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arXiv2017

A Universal Counting of Black Hole Microstates in AdS$_4$

Many three-dimensional $\mathcal{N}=2$ SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS$_4$ magnetically charged black holes in M-theory and massive type IIA string theory. In this context we also discuss novel AdS$_2$ solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.

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arXiv2017

Superconformal Blocks for SCFTs with Eight Supercharges

We show how to treat the superconformal algebras with eight Poincaré supercharges in a unified manner for spacetime dimension $2 < d\leq 6$. This formalism is ideally suited for analyzing the quadratic Casimir operator of the superconformal algebra and its use in deriving superconformal blocks. We illustrate this by an explicit construction of the superconformal blocks, for any value of the spacetime dimension, for external protected scalar operators which are the lowest component of flavor current multiplets.

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arXiv2017

Holography, Brane Intersections and Six-dimensional SCFTs

We study supersymmetric intersections of NS5-, D6- and D8-branes in type IIA string theory. We focus on the supergravity description of this system and identify a "near horizon" limit in which we recover the recently classified supersymmetric seven-dimensional AdS solutions of massive type IIA supergravity. Using a consistent truncation to seven-dimensional gauged supergravity we construct a universal supersymmetric deformation of these AdS vacua. In the holographic dual six-dimensional (1,0) superconformal field theory this deformation describes a universal RG flow on the tensor branch of the vacuum moduli space triggered by a vacuum expectation value for a protected scalar operator of dimension four.

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arXiv2017

Comments on Squashed-sphere Partition Functions

We study the partition function of odd-dimensional conformal field theories placed on spheres with a squashed metric. We establish that the round sphere provides a local extremum for the free energy which, in general, is not a global extremum. In addition, we show that the leading quadratic correction to the free energy around this extremum is proportional to the coefficient, $C_T$, determining the two-point function of the energy-momentum tensor in the CFT. For three-dimensional CFTs, we compute explicitly this proportionality constant for a class of squashing deformations which preserve an $SU(2)\times U(1)$ isometry group on the sphere. In addition, we evaluate the free energy as a function of the squashing parameter for theories of free bosons, free fermions, as well as CFTs holographically dual to Einstein gravity with a negative cosmological constant. We observe that, after suitable normalization, the dependence of the free energy on the squashing parameter for all these theories is nearly universal for a large region of parameter space and is well approximated by a simple quadratic function arising from holography. We generalize our results to five-dimensional CFTs and, in this context, we also study theories holographically dual to six-dimensional Gauss-Bonnet gravity.

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arXiv2016

The NUTs and Bolts of Squashed Holography

We evaluate the partition function of the free O(N) model on a two-parameter family of squashed three spheres. We also find new solutions of general relativity with negative cosmological constant and the same double squashed boundary geometry and analyse their thermodynamic properties. Remarkably, both systems exhibit a qualitatively similar behaviour over the entire configuration space of boundary geometries. Recent formulations of dS/CFT enable one to interpret the field theory partition function as a function of the two squashing parameters as the Hartle-Hawking wave function in a minisuperspace model of anisotropic deformations of de Sitter space. The resulting probability distribution is normalisable and globally peaked at the round three sphere, with a low amplitude of boundary geometries with negative scalar curvature.

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arXiv2016

Two-dimensional SCFTs from D3-branes

We find a large class of two-dimensional $\mathcal{N}=(0,2)$ SCFTs obtained by compactifying four-dimensional $\mathcal{N}=1$ quiver gauge theories on a Riemann surface. We study these theories using anomalies and $c$-extremization. The gravitational duals to these fixed points are new AdS$_3$ solutions of IIB supergravity which we exhibit explicitly. Along the way we uncover a universal relation between the conformal anomaly coefficients of four-dimensional and two-dimensional SCFTs connected by an RG flow across dimensions. We also observe an interesting novel phenomenon in which the superconformal R-symmetry mixes with baryonic symmetries along the RG flow.

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arXiv2016

Holography for $\mathcal{N}=1^*$ on $S^4$

We construct the five-dimensional supergravity dual of the $\mathcal{N}=1^*$ mass deformation of the $\mathcal{N} =4$ supersymmetric Yang-Mills theory on $S^4$ and use it to calculate the universal contribution to the corresponding $S^4$ free energy at large 't Hooft coupling in the planar limit. The holographic RG flow solutions are smooth and preserve four supercharges. As a novel feature compared to the holographic duals of $\mathcal{N} = 1^*$ on $\mathbb{R}^4$, in our backgrounds the five-dimensional dilaton has a non-trivial profile, and the gaugino condensate is fixed in terms of the mass-deformation parameters. Important aspects of the analysis involve characterizing the ambiguities in the partition function of non-conformal $\mathcal{N}=1$ supersymmetric theories on $S^4$ as well as the action of S-duality on the $\mathcal{N}=1^*$ theory.

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arXiv2016

Supersymmetric Casimir Energy and the Anomaly Polynomial

We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology $S^1\times S^{D-1}$ is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.

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arXiv2015

Bootstrapping SCFTs with Four Supercharges

We study the constraints imposed by superconformal symmetry, crossing symmetry, and unitarity for theories with four supercharges in spacetime dimension $2\leq d\leq 4$. We show how superconformal algebras with four Poincaré supercharges can be treated in a formalism applicable to any, in principle continuous, value of $d$ and use this to construct the superconformal blocks for any $d\leq 4$. We then use numerical bootstrap techniques to derive upper bounds on the conformal dimension of the first unprotected operator appearing in the OPE of a chiral and an anti-chiral superconformal primary. We obtain an intriguing structure of three distinct kinks. We argue that one of the kinks smoothly interpolates between the $d=2$, $\mathcal N=(2,2)$ minimal model with central charge $c=1$ and the theory of a free chiral multiplet in $d=4$, passing through the critical Wess-Zumino model with cubic superpotential in intermediate dimensions.

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arXiv2015

Bootstrapping the Three-Dimensional Supersymmetric Ising Model

We implement the conformal bootstrap program for three-dimensional CFTs with $\mathcal{N}=2$ supersymmetry and find universal constraints on the spectrum of operator dimensions in these theories. By studying the bounds on the dimension of the first scalar appearing in the OPE of a chiral and an anti-chiral primary, we find a kink at the expected location of the critical three-dimensional $\mathcal{N}=2$ Wess-Zumino model, which can be thought of as a supersymmetric analog of the critical Ising model. Focusing on this kink, we determine, to high accuracy, the low-lying spectrum of operator dimensions of the theory.

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arXiv2014

(0,2) SCFTs from the Leigh-Strassler Fixed Point

We show that there is a family of two-dimensional $(0,2)$ SCFTs associated with twisted compactifications of the four-dimensional $\mathcal{N}=1$ Leigh-Strassler fixed point on a closed hyperbolic Riemann surface. We calculate the central charges for this class of theories using anomalies and $c$-extremization. In a suitable truncation of the five-dimensional maximal supergravity, we construct supersymmetric $AdS_3$ solutions that are holographic duals of those two-dimensional $(0,2)$ SCFTs. We also exhibit supersymmetric domain wall solutions that are holographically dual to the RG flows between the four-dimensional and two-dimensional theories.

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arXiv2013

Dilaton Effective Action with $\mathcal{N}=1$ Supersymmetry

We clarify the structure of the four-dimensional low-energy effective action that encodes the conformal and $U(1)$ R-symmetry anomalies in an $\mathcal{N}=1$ supersymmetric field theory. The action depends on the dilaton, $τ$, associated with broken conformal symmetry, and the Goldstone mode, $β$, of the broken $U(1)$ R-symmetry. We present the action for general curved spacetime and background gauge field up to and including all possible four-derivative terms. The result, constructed from basic principles, extends and clarifies the structure found by Schwimmer and Theisen in arXiv:1011.0696 using superfield methods. We show that the Goldstone mode $β$ does not interfere with the proof of the four-dimensional $a$-theorem based on $2 \to 2$ dilaton scattering. In fact, supersymmetry Ward identities ensure that a proof of the $a$-theorem can also be based on $2 \to 2$ Goldstone mode scattering when the low-energy theory preserves $\mathcal{N}=1$ supersymmetry. We find that even without supersymmetry, a Goldstone mode for any broken global $U(1)$ symmetry cannot interfere with the proof of the four-dimensional $a$-theorem.

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arXiv2013

Supersymmetric Janus Solutions in Four Dimensions

We use maximal gauged supergravity in four dimensions to construct the gravity dual of a class of supersymmetric conformal interfaces in the theory on the world-volume of multiple M2-branes. We study three classes of examples in which the $(1+1)$-dimensional defects preserve $(4,4)$, $(0,2)$ or $(0,1)$ supersymmetry. Many of the solutions have the maximally supersymmetric $AdS_4$ vacuum dual to the $\mathcal{N}=8$ ABJM theory on both sides of the interface. We also find new special classes of solutions including one that interpolates between the maximally supersymmetric vacuum and a conformal fixed point with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. We find another solution that interpolates between two distinct conformal fixed points with $\mathcal{N}=1$ supersymmetry and $G_2$ global symmetry. In eleven dimensions, this $G_2$ to $G_2$ solution corresponds to a domain wall across which a magnetic flux reverses orientation.

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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

Linear Quivers and N=1 SCFTs from M5-branes

We study a class of N=1 quiver gauge theories build out of vector multiplets and matter multiplets in the fundamental and bifundamental representations. We argue that these theories flow to interacting SCFTs in the IR and calculate their central charges. We exhibit a type IIA brane construction which at low energies is described by these SCFTs. This also leads to a natural description of the theories in terms of M5-branes on a punctured sphere.

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arXiv2013

Two-dimensional SCFTs from wrapped branes and c-extremization

We apply c-extremization, whose proof we review in full detail, to study two-dimensional N=(0,2) superconformal field theories arising from the low-energy dynamics of D3-branes wrapped on Riemann surfaces and M5-branes wrapped on four-manifolds. We compute the exact central charges of these theories using anomalies and c-extremization. In all cases we also construct AdS_3 supergravity solutions of type IIB and eleven-dimensional supergravity, which are holographic duals to the field theories at large N, and exactly reproduce the central charges computed via c-extremization.

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arXiv2013

Exact two-dimensional superconformal R-symmetry and c-extremization

We uncover a general principle, dubbed c-extremization, which determines the exact R-symmetry of a two-dimensional unitary superconformal field theory with N=(0,2) supersymmetry. To illustrate its utility, we study superconformal theories obtained by twisted compactifications of four-dimensional N=4 super-Yang-Mills on Riemann surfaces, and construct their gravity duals.

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