arXiv subjects

Davide Cassani

Publications and source records attributed to Davide Cassani.

At least 37 records · Page 2Linked to original sources

arXiv2018

Squashing the Boundary of Supersymmetric AdS$_5$ Black Holes

We construct new supersymmetric black holes in five-dimensional supergravity with an arbitrary number of vector multiplets and Fayet-Iliopoulos gauging. These are asymptotically locally AdS$_5$ and the conformal boundary comprises a squashed three-sphere with $\text{SU}(2)\times \text{U}(1)$ symmetry. The solution depends on two parameters, of which one determines the angular momentum and the Page electric charges, while the other controls the squashing at the boundary. The latter is arbitrary, however in the flow towards the horizon it is attracted to a value that only depends on the other parameter of the solution. The entropy is reproduced by a simple formula involving the angular momentum and the Page charges, rather than the holographic charges. Choosing the appropriate five-dimensional framework, the solution can be uplifted to type IIB supergravity on $S^5$ and should thus be dual to $\mathcal{N}=4$ super Yang-Mills on a rotating, squashed Einstein universe.

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arXiv2018

Holographic RG Flows for Four-dimensional $\mathcal{N}=2$ SCFTs

We study holographic renormalization group flows from four-dimensional $\mathcal{N}=2$ SCFTs to either $\mathcal{N}=2$ or $\mathcal{N}=1$ SCFTs. Our approach is based on the framework of five-dimensional half-maximal supergravity with general gauging, which we use to study domain wall solutions interpolating between different supersymmetric AdS$_5$ vacua. We show that a holographic RG flow connecting two $\mathcal{N}=2$ SCFTs is only possible if the flavor symmetry of the UV theory admits an ${\rm SO}(3)$ subgroup. In this case the ratio of the IR and UV central charges satisfies a universal relation which we also establish in field theory. In addition we provide several general examples of holographic flows from $\mathcal{N}=2$ to $\mathcal{N}=1$ SCFTs and relate the ratio of the UV and IR central charges to the conformal dimension of the operator triggering the flow. Instrumental to our analysis is a derivation of the general conditions for AdS vacua preserving eight supercharges as well as for domain wall solutions preserving eight Poincare supercharges in half-maximal supergravity.

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arXiv2017

Supersymmetry on curved spaces and superconformal anomalies

We study the consequences of unbroken rigid supersymmetry of four-dimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the R-current is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite R-charge are preserved, otherwise the (anti-)self-dual part of the vector field-strength is fixed by the Weyl tensor. As a result of this relation, the trace and R-current anomalies of superconformal field theories simplify, with the trace anomaly becoming purely topological. In particular, in Lorentzian signature, or in the presence of two Euclidean supercharges of opposite R-charge, supersymmetry of the background implies that the term proportional to the central charge c vanishes, both in the trace and R-current anomalies. This is equivalent to the vanishing of a superspace Weyl invariant. We comment on the implications of our results for holography.

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arXiv2017

Holographic renormalization and supersymmetry

Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a supersymmetric renormalization scheme. Recent results in localization have brought this question into sharp focus: rigid supersymmetry on a curved boundary requires specific geometric structures, and general arguments imply that BPS observables, such as the partition function, are invariant under certain deformations of these structures. One can then ask if the dual holographic observables are similarly invariant. We study this question in minimal N = 2 gauged supergravity in four and five dimensions. In four dimensions we show that holographic renormalization precisely reproduces the expected field theory results. In five dimensions we find that no choice of standard holographic counterterms is compatible with supersymmetry, which leads us to introduce novel finite boundary terms. For a class of solutions satisfying certain topological assumptions we provide some independent tests of these new boundary terms, in particular showing that they reproduce the expected VEVs of conserved charges.

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arXiv2016

The holographic supersymmetric Casimir energy

We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges.

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arXiv2016

Exceptional generalised geometry for massive IIA and consistent reductions

We develop an exceptional generalised geometry formalism for massive type IIA supergravity. In particular, we construct a deformation of the generalised Lie derivative, which generates the type IIA gauge transformations as modified by the Romans mass. We apply this new framework to consistent Kaluza-Klein reductions preserving maximal supersymmetry. We find a generalised parallelisation of the exceptional tangent bundle on S^6, and from this reproduce the consistent truncation ansatz and embedding tensor leading to dyonically gauged ISO(7) supergravity in four dimensions. We also discuss closely related hyperboloid reductions, yielding a dyonic ISO(p,7-p) gauging. Finally, while for vanishing Romans mass we find a generalised parallelisation on S^d, d=4,3,2, leading to a maximally supersymmetric reduction with gauge group SO(d+1) (or larger), we provide evidence that an analogous reduction does not exist in the massive theory.

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arXiv2016

Comments on supersymmetric solutions of minimal gauged supergravity in five dimensions

We investigate supersymmetric solutions of minimal gauged supergravity in five dimensions, in the timelike class. We propose an ansatz based on a four-dimensional local orthotoric Kaehler metric and reduce the problem to a single sixth-order equation for two functions, each of one variable. We find an analytic, asymptotically locally AdS solution comprising five parameters. For a conformally flat boundary, this reduces to a previously known solution with three parameters, representing the most general solution of this type known in the minimal theory. We discuss the possible relevance of certain topological solitons contained in the latter to account for the supersymmetric Casimir energy of dual superconformal field theories on S^3 x R. Although we obtain a negative response, our analysis clarifies several aspects of these solutions. In particular, we show that there exists a unique regular topological soliton in this family.

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arXiv2015

The Casimir Energy in Curved Space and its Supersymmetric Counterpart

We study $d$-dimensional Conformal Field Theories (CFTs) on the cylinder, $S^{d-1}\times \mathbb{R}$, and its deformations. In $d=2$ the Casimir energy (i.e. the vacuum energy) is universal and is related to the central charge $c$. In $d=4$ the vacuum energy depends on the regularization scheme and has no intrinsic value. We show that this property extends to infinitesimally deformed cylinders and support this conclusion with a holographic check. However, for $\mathcal{N}=1$ supersymmetric CFTs, a natural analog of the Casimir energy turns out to be scheme independent and thus intrinsic. We give two proofs of this result. We compute the Casimir energy for such theories by reducing to a problem in supersymmetric quantum mechanics. For the round cylinder the vacuum energy is proportional to $a+3c$. We also compute the dependence of the Casimir energy on the squashing parameter of the cylinder. Finally, we revisit the problem of supersymmetric regularization of the path integral on Hopf surfaces.

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arXiv2014

Supersymmetric counterterms from new minimal supergravity

We present a systematic classification of counterterms of four-dimensional supersymmetric field theories on curved space, obtained as the rigid limit of new minimal supergravity. These are supergravity invariants constructed using the field theory background fields. We demonstrate that if the background preserves two supercharges of opposite chirality, then all dimensionless counterterms vanish, implying that in this case the supersymmetric partition function is free of ambiguities. When only one Euclidean supercharge is preserved, we describe the ambiguities that appear in the partition function, in particular in the dependence on marginal couplings.

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arXiv2014

The gravity dual of supersymmetric gauge theories on a squashed $S^1 \times S^3$

We present a new one-parameter family of supersymmetric solutions deforming AdS_5. This is constructed as an asymptotically locally anti de Sitter (AlAdS) solution of five-dimensional minimal gauged supergravity, with topology R x R^4 and a non-trivial graviphoton field, and can be uplifted to ten or eleven dimensional supergravities. An analytic continuation of this solution yields the gravity dual to a class of four-dimensional N=1 supersymmetric gauge theories on a curved manifold with topology S^1 x S^3, comprising an SU(2) x U(1)-symmetric squashed three-sphere, with a non-trivial background gauge field coupling to the R-symmetry current. We compute the holographically renormalised on-shell action and interpret it in terms of the Casimir energy of the dual field theory. We also determine the holographic conserved charges of the solution and discuss relations between them.

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arXiv2014

Localization on Hopf surfaces

We discuss localization of the path integral for supersymmetric gauge theories with an R-symmetry on Hermitian four-manifolds. After presenting the localization locus equations for the general case, we focus on backgrounds with S^1 x S^3 topology, admitting two supercharges of opposite R-charge. These are Hopf surfaces, with two complex structure moduli p,q. We compute the localized partition function on such Hopf surfaces, allowing for a very large class of Hermitian metrics, and prove that this is proportional to the supersymmetric index with fugacities p,q. Using zeta function regularisation, we determine the exact proportionality factor, finding that it depends only on p,q, and on the anomaly coefficients a, c of the field theory. This may be interpreted as a supersymmetric Casimir energy, and provides the leading order contribution to the partition function in a large N expansion.

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arXiv2014

Supersymmetry in Lorentzian Curved Spaces and Holography

We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal theory is equivalent to the existence of a charged conformal Killing spinor. Differently from the Euclidean case, we show that the existence of such spinors is equivalent to the existence of a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, this vector field is further restricted to be Killing. We demonstrate how these results agree with the existing classification of supersymmetric solutions of minimal gauged supergravity in five dimensions.

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arXiv2013

BPS domain walls in N=4 supergravity and dual flows

We establish the conditions for supersymmetric domain wall solutions to N=4 gauged supergravity in five dimensions. These read as BPS first-order equations for the warp factor and the scalar fields, driven by a superpotential and supplemented by a set of constraints that we specify in detail. Then we apply our results to certain consistent truncations of IIB supergravity, thus exploring their dual field theory renormalization group flows. We find a universal flow deforming superconformal theories on D3-branes at Calabi-Yau cones. Moreover, we obtain a superpotential for the solution corresponding to the baryonic branch of the Klebanov-Strassler theory, as well as the superpotential for the flow describing D3 and wrapped D5-branes on the resolved conifold.

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arXiv2012

All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua

We study consistent truncations of M-theory to gauged N=2 supergravity in four dimensions, based on a large class of SU(3)-structures in seven dimensions. We show that the gauging involves isometries of the vector multiplet scalar manifold as well as the Heisenberg algebra and a special isometry of the hyperscalar manifold. As a result, non-abelian gauge groups and new non-trivial scalar potentials are generated. Then we specialize to all homogeneous SU(3)-structures supporting supersymmetric AdS4 vacua. These are the Stiefel manifold V52, the Aloff-Wallach spaces N(k,l), the seven-sphere (seen as SU(4)/SU(3) or Sp(2)/Sp(1)) and the M110 and Q111 coset spaces. For each of these cases, we describe in detail the N=2 model and discuss its peculiarities.

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arXiv2011

Tri-Sasakian consistent reduction

We establish a universal consistent Kaluza-Klein truncation of M-theory based on seven-dimensional tri-Sasakian structure. The four-dimensional truncated theory is an N=4 gauged supergravity with three vector multiplets and a non-abelian gauge group, containing the compact factor SO(3). Consistency follows from the fact that our truncation takes exactly the same form as a left-invariant reduction on a specific coset manifold, and we show that the same holds for the various universal consistent truncations recently put forward in the literature. We describe how the global symmetry group SL(2,R) x SO(6,3) is embedded in the symmetry group E7(7) of maximally supersymmetric reductions, and make the connection with the approach of Exceptional Generalized Geometry. Vacuum AdS4 solutions spontaneously break the amount of supersymmetry from N=4 to N=3,1 or 0, and the spectrum contains massive modes. We find a subtruncation to minimal N=3 gauged supergravity as well as an N=1 subtruncation to the SO(3)-invariant sector. We also show that a reduction on the homogeneous space N^{010} enhances the universal tri-Sasakian truncation with a Betti vector multiplet.

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arXiv2011

Constructing Lifshitz solutions from AdS

Under general assumptions, we show that a gravitational theory in d+1 dimensions admitting an AdS solution can be reduced to a d-dimensional theory containing a Lifshitz solution with dynamical exponent z=2. Working in a d=4, N=2 supergravity setup, we prove that if the AdS background is N=2 supersymmetric, then the Lifshitz geometry preserves 1/4 of the supercharges, and we construct the corresponding Killing spinors. We illustrate these results in examples from supersymmetric consistent truncations of type IIB supergravity, enhancing the class of known 4-dimensional Lifshitz solutions of string theory. As a byproduct, we find a new AdS4 x S1 x T(1,1) solution of type IIB.

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arXiv2011

Consistent truncations with massive modes and holography

We review the basic features of some recently found consistent Kaluza-Klein truncations including massive modes. We emphasize the general ideas underlying the reduction procedure, then we focus on type IIB supergravity on 5-dimensional manifolds admitting a Sasaki-Einstein structure, which leads to half-maximal gauged supergravity in five dimensions. Finally, we comment on the holographic picture of consistency.

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arXiv2010

A supersymmetric consistent truncation for conifold solutions

We establish a supersymmetric consistent truncation of type IIB supergravity on the T^{1,1} coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)xSU(2) invariant Kaluza-Klein modes. The five-dimensional model is a gauged N=4 supergravity with three vector multiplets, which incorporates various conifold solutions and is suitable for the study of their dynamics. By analysing the scalar potential we find a family of new non-supersymmetric AdS_5 extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T^{1,1} different from the standard one. Finally, we discuss some simple consistent subtruncations preserving N=2 supersymmetry. One of them still contains the Klebanov-Strassler solution, and is compatible with the inclusion of smeared D7-branes.

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