arXiv subjects

Seyed Morteza Hosseini

Publications and source records attributed to Seyed Morteza Hosseini.

34 records · Page 2Linked to original sources

arXiv2019

Geometry of $\mathcal{I}$-extremization and black holes microstates

The entropy of a class of asymptotically AdS$_4$ magnetically charged BPS black holes can be obtained by extremizing the topologically twisted index of the dual three-dimensional field theory. This principle is known as $\mathcal{I}$-extremization. A gravitational dual of $\mathcal{I}$-extremization for a class of theories obtained by twisted compactifications of M2-branes living at a Calabi-Yau four-fold has been recently proposed. In this paper we investigate the relation between the two extremization principles. We show that the two extremization procedures are equivalent for theories without baryonic symmetries, which include ABJM and the theory dual to the non-toric Sasaki-Einstein manifold $V^{5,2}$. We then consider a class of quivers dual to M2-branes at toric Calabi-Yau four-folds for which the $\mathcal{I}$-functional can be computed in the large $N$ limit, and depends on three mesonic fluxes. We propose a gravitational dual for this construction, that we call mesonic twist, and we show that the gravitational extremization problem and $\mathcal{I}$-extremization are equivalent. We comment on more general cases.

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arXiv2019

Proving the equivalence of $c$-extremization and its gravitational dual for all toric quivers

The gravitational dual of $c$-extremization for a class of $(0,2)$ two-dimensional theories obtained by twisted compactifications of D3-brane gauge theories living at a toric Calabi-Yau three-fold has been recently proposed. The equivalence of this construction with $c$-extremization has been checked in various examples and holds also off-shell. In this note we prove that such equivalence holds for an arbitrary toric Calabi-Yau. We do it by generalizing the proof of the equivalence between $a$-maximization and volume minimization for four-dimensional toric quivers. By an explicit parameterization of the R-charges we map the trial right-moving central charge $c_r$ into the off-shell functional to be extremized in gravity. We also observe that the similar construction for M2-branes on $\mathbb{C}^4$ is equivalent to the $\mathcal{I}$-extremization principle that leads to the microscopic counting for the entropy of magnetically charged black holes in AdS$_4\times S^7$. Also this equivalence holds off-shell.

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arXiv2018

6D attractors and black hole microstates

We find a family of AdS$_2\times \mathcal{M}_4$ supersymmetric solutions of the six-dimensional $\mathrm{F}(4)$ gauged supergravity coupled to one vector multiplet that arises as a low energy description of massive type IIA supergravity on (warped) AdS$_6\times S^4$. $\mathcal{M}_4$ is either a Kähler-Einstein manifold or a product of two Riemann surfaces with a constant curvature metric. These solutions correspond to the near-horizon region of a family of static magnetically charged black holes. In the case where $\mathcal{M}_4$ is a product of Riemann surfaces, we successfully compare their entropy to a microscopic counting based on the recently computed topologically twisted index of the five-dimensional $\mathcal{N}=1$ $\mathrm{USp}(2 N)$ theory with $N_f$ fundamental flavors and an antisymmetric matter field. Furthermore, our results suggest that the near-horizon regions exhibit an attractor mechanism for the scalars in the matter coupled $\mathrm{F}(4)$ gauged supergravity, and we give a proposal for it.

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arXiv2018

Topologically twisted indices in five dimensions and holography

We provide a formula for the partition function of five-dimensional $\mathcal{N}=1$ gauge theories on $\mathcal{M}_4 \times S^1$, topologically twisted along $\mathcal{M}_4$ in the presence of general background magnetic fluxes, where $\mathcal{M}_4$ is a toric Kähler manifold. The result can be expressed as a contour integral of the product of copies of the K-theoretic Nekrasov's partition function, summed over gauge magnetic fluxes. The formula generalizes to five dimensions the topologically twisted index of three- and four-dimensional field theories. We analyze the large $N$ limit of the partition function and some related quantities for two theories: $\mathcal{N}=2$ SYM and the $\mathrm{USp}(2N)$ theory with $N_f$ flavors and an antisymmetric matter field. For $\mathbb{P}^1 \times \mathbb{P}^1 \times S^1$, which can be easily generalized to $Σ_{\mathfrak{g}_2} \times Σ_{\mathfrak{g}_1} \times S^1$, we conjecture the form of the relevant saddle point at large $N$. The resulting partition function for $\mathcal{N}=2$ SYM scales as $N^3$ and is in perfect agreement with the holographic results for domain walls in AdS$_7 \times S^4$. The large $N$ partition function for the $\mathrm{USp}(2N)$ theory scales as $N^{5/2}$ and gives a prediction for the entropy of a class of magnetically charged black holes in massive type IIA supergravity.

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arXiv2018

Black hole microstates and supersymmetric localization

This thesis focuses mainly on understanding the origin of the Bekenstein-Hawking entropy for a class of four- and five-dimensional BPS black holes in string/M-theory. To this aim, important ingredients are holography and supersymmetric localization. Using the method of supersymmetric localization, the Euclidean path integrals for supersymmetric field theories on $Σ_\mathfrak{g} \times T^{n}$ $(n=1,2)$, with at least four real supercharges, can be reduced to a matrix integral that depends on background magnetic fluxes and chemical potentials for the global symmetries of the theory. This defines the topologically twisted index which, upon extremization with respect to the chemical potentials, is conjectured to reproduce the entropy of magnetically charged static BPS AdS$_{4/5}$ black holes/strings. We solve a number of such matrix models both in three and four dimensions and provide general formulae in the large $N$ limit. We then use these results to provide the microscopic realization of the entropy of a class of BPS black holes in $\mathcal{N}=2$ gauged supergravity. Finally, inspired by our previous results, we put forward an extremization principle for reproducing the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS$_5\times S^5$.

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arXiv2018

The Cardy limit of the topologically twisted index and black strings in AdS$_5$

We evaluate the topologically twisted index of a general four-dimensional $\mathcal{N} = 1$ gauge theory in the "high-temperature" limit. The index is the partition function for $\mathcal{N} = 1$ theories on $S^2 \times T^2$, with a partial topological twist along $S^2$, in the presence of background magnetic fluxes and fugacities for the global symmetries. We show that the logarithm of the index is proportional to the conformal anomaly coefficient of the two-dimensional $\mathcal{N} = (0,2)$ SCFTs obtained from the compactification on $S^2$. We also present a universal formula for extracting the index from the four-dimensional conformal anomaly coefficient and its derivatives. We give examples based on theories whose holographic duals are black strings in type IIB backgrounds AdS$_5 \times \text{SE}_5$, where SE$_5$ are five-dimensional Sasaki-Einstein spaces.

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arXiv2018

Large $N$ matrix models for 3d ${\cal N}=2$ theories: twisted index, free energy and black holes

We provide general formulae for the topologically twisted index of a general three-dimensional ${\cal N}\geq 2$ gauge theory with an M-theory or massive type IIA dual in the large $N$ limit. The index is defined as the supersymmetric path integral of the theory on $S^2\times S^1$ in the presence of background magnetic fluxes for the R- and global symmetries and it is conjectured to reproduce the entropy of magnetically charged static BPS AdS$_4$ black holes. For a class of theories with an M-theory dual, we show that the logarithm of the index scales indeed as $N^{3/2}$ (and $N^{5/3}$ in the massive type IIA case). We find an intriguing relation with the (apparently unrelated) large $N$ limit of the partition function on $S^3$. We also provide a universal formula for extracting the index from the large $N$ partition function on $S^3$ and its derivatives and point out its analogy with the attractor mechanism for AdS black holes.

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arXiv2018

Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces

In this paper, we calculate the topological free energy for a number of ${\mathcal N} \geq 2$ Yang-Mills-Chern-Simons-matter theories at large $N$ and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on $S^2 \times S^1$ with a topological A-twist along $S^2$ and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over various well-known homogeneous Sasaki-Einstein seven-manifolds, $N^{0,1,0}$, $V^{5,2}$, and $Q^{1,1,1}$. We check that the large $N$ topological free energy can be matched for theories which are related by dualities, including mirror symmetry and $\mathrm{SL}(2,\mathbb{Z})$ duality.

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arXiv2018

A note on the entropy of rotating BPS AdS$_7\times S^4$ black holes

In this note we show that the entropy of BPS, rotating, electrically charged AdS$_7 \times S^4$ black holes can be obtained by an extremization principle involving a particular combination of anomaly coefficients of the six-dimensional $\mathcal{N} = (2, 0)$ theory. This result extends our previous finding for BPS, rotating AdS$_5 \times S^5$ black holes.

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arXiv2017

Holographic microstate counting for AdS$_4$ black holes in massive IIA supergravity

We derive the Bekenstein-Hawking entropy for a class of BPS black holes in the massive type IIA supergravity background AdS$_4 \times S^6$ from a microscopic counting of supersymmetric ground states in a holographically dual field theory. The counting is performed by evaluating the topologically twisted index of three-dimensional $\mathcal{N}=2$ Chern-Simons-matter gauge theories in the large $N$ limit. The $\mathcal{I}$-extremization principle is shown to match the attractor mechanism for the near-horizon geometries constructed in the four-dimensional dyonic $\mathcal{N}=2$ gauged supergravity, that arises as a consistent truncation of massive type IIA supergravity on $S^6$. In particular, our results prove that the imaginary part of the three-dimensional partition functions plays a crucial rôle in holography.

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arXiv2017

Entanglement and mutual information in two-dimensional nonrelativistic field theories

We carry out a systematic study of entanglement entropy in nonrelativistic conformal field theories via holographic techniques. After a discussion of recent results concerning Galilean conformal field theories, we deduce a novel expression for the entanglement entropy of (1+1)-dimensional Lifshitz field theories --- this is done both at zero and finite temperature. Based on these results, we pose a conjecture for the anomaly coefficient of a Lifshitz field theory dual to new massive gravity. It is found that the Lifshitz entanglement entropy at finite temperature displays a striking similarity with that corresponding to a flat space cosmology in three dimensions. We claim that this structure is an inherent feature of the entanglement entropy for nonrelativistic conformal field theories. We finish by exploring the behavior of the mutual information for such theories.

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arXiv2017

An extremization principle for the entropy of rotating BPS black holes in AdS$_5$

We show that the Bekenstein-Hawking entropy of a class of BPS electrically charged rotating black holes in AdS$_5\times S^5$ can be obtained by a simple extremization principle. We expect that this extremization corresponds to the attractor mechanism for BPS rotating black holes in five-dimensional gauged supergravity, which is still unknown. The expression to be extremized has a suggestive resemblance to anomaly polynomials and the supersymmetric Casimir energy recently studied for $\mathcal{N}=4$ super Yang-Mills.

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arXiv2016

Gravitational anomalies, entanglement entropy, and flat-space holography

We introduce a prescription to compute the entanglement entropy of Galilean conformal field theories by combining gravitational anomalies and an İnönü-Wigner contraction. We find that our expression for the entanglement entropy in the thermal limit reproduces the Cardy formula for Galilean conformal field theories. Using this proposal, we calculate the entanglement entropy for a class of Galilean conformal field theories, which are believed to be dual to three-dimensional flat-space cosmological solutions. These geometries describe expanding (contracting) universes and can be viewed as the flat-space limit of rotating Bañados-Teitelboim-Zanelli black holes. We show that our finding reduces, in the appropriate limits, to the results discussed in the literature and provide interpretations for the previously unexplored regimes, such as flat-space chiral gravity.

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arXiv2015

Free-kick condition for entanglement entropy in higher curvature gravity

In order to compute the entanglement entropy for a given region in a theory with an Einstein gravity dual, the Ryu-Takayanagi prescription tells us that we must compute the the area of an extremal surface anchored to the entangling region. However, if the dual gravity theory receives higher-curvature corrections we are compelled to extremize a quantity which is no longer given by the area but a higher-derivative functional. Hence, in order to find the extremal surface that yields the correct value of the entanglement entropy, we must include an additional boundary condition to the problem. We claim that the additional condition can be fixed by demanding that the relationship between the bulk depth and the size of the entangling region is the one induced by geodesics, we call this the free-kick condition. We implement this prescription in the computation of the entanglement entropy of the hairy black hole in new massive gravity, and find a perfect agreement with conformal field theory expectations.

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arXiv2015

Holography of 3D Asymptotically Flat Black Holes

We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS$_{3}$ group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.

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arXiv2014

One-loop quantum correction to the mass of the supersymmetric Kink in (1 + 1) dimensions using the exact spectra and the phase shifts

We compute the quantum correction to the mass of the kink at the one-loop level in (1+1) dimensions with minimal supersymmetry. In this paper we discuss this issue from the Casimir energy perspective using phase shifts along with the mode number cut-off regularization method. Exact solutions and in particular an exact expression for the phase shifts are already available for the bosonic sector. In this paper we derive analogous exact results for the fermionic sector. Most importantly, we derive a unique and exact expression for the fermionic phase shift, using the exact solutions for the continuum parts of the spectrum and a prescription we had introduced earlier. We use the strong and weak forms of the Levinson theorem merely for checking the consistency of our phase shifts and results, and not as an integral part of our procedure. Moreover, we find that the properties of the fermionic spectrum, including bound and continuum states, are independent of the magnitude of the Yukawa coupling constant $λ$, and that the dynamical mass generation occurs at the tree level. These are all due to SUSY and are in sharp contrast to analogous models without SUSY, such as the Jackiw-Rebbi model, where $λ$ is a free parameter. We use the renormalized perturbation theory and find the counterterm which is consistent with supersymmetry. We show that this procedure is sufficient to obtain the accepted value for the one-loop quantum correction to the mass of the SUSY kink which is $-\frac{m}{2π}$.

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