Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userToric geometry and the dual of ${cal I}$-extremization
157
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider $d=3$, $mathcal{N}=2$ gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, $Sigma_g$, with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a $D=11$ supergravity dual of the form AdS$_2times Y_9$, with electric four-form flux and where $Y_9$ is topologically a fibration of a Sasakian $Y_7$ over $Sigma_g$. These $D=11$ solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS$_4times Y_7$, with a Sasaki-Einstein metric on $Y_7$. We show that an off-shell entropy function for the dual AdS$_2$ solutions may be computed using the toric data and Kahler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of $Y_7$ over $Sigma_g$ and a Kahler class parameter for $Sigma_g$. We also discuss the class of supersymmetric AdS$_3times Y_7$ solutions of type IIB supergravity with five-form flux only in the case that $Y_7$ is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning ${cal I}$-extremization.
rate research
Read More
In this paper we provide a first attempt towards a toric geometric interpretation of scattering amplitudes. In recent investigations it has indeed been proposed that the all-loop integrand of planar N=4 SYM can be represented in terms of well defined finite objects called on-shell diagrams drawn on disks. Furthermore it has been shown that the physical information of on-shell diagrams is encoded in the geometry of auxiliary algebraic varieties called the totally non negative Grassmannians. In this new formulation the infinite dimensional symmetry of the theory is manifest and many results, that are quite tricky to obtain in terms of the standard Lagrangian formulation of the theory, are instead manifest. In this paper, elaborating on previous results, we provide another picture of the scattering amplitudes in terms of toric geometry. In particular we describe in detail the toric varieties associated to an on-shell diagram, how the singularities of the amplitudes are encoded in some subspaces of the toric variety, and how this picture maps onto the Grassmannian description. Eventually we discuss the action of cluster transformations on the toric varieties. The hope is to provide an alternative description of the scattering amplitudes that could contribute in the developing of this very interesting field of research.
We study the holographic dual to $c$-extremization for 2d $(0,2)$ superconformal field theories (SCFTs) that have an AdS$_3$ dual realized in Type IIB with varying axio-dilaton, i.e. F-theory. M/F-duality implies that such AdS$_3$ solutions can be mapped to AdS$_2$ solutions in M-theory, which are holographically dual to superconformal quantum mechanics (SCQM), obtained by dimensional reduction of the 2d SCFTs. We analyze the corresponding map between holographic $c$-extremization in F-theory and $mathcal{I}$-extremization in M-theory, where in general the latter receives corrections relative to the F-theory result.
It has recently been claimed that a Cardy-like limit of the superconformal index of 4d $mathcal{N}=4$ SYM accounts for the entropy function, whose Legendre transform corresponds to the entropy of the holographic dual AdS$_5$ rotating black hole. Here we study this Cardy-like limit for $mathcal{N}=1$ toric quiver gauge theories, observing that the corresponding entropy function can be interpreted in terms of the toric data. Furthermore, for some families of models, we compute the Legendre transform of the entropy function, comparing with similar results recently discussed in the literature.
Compactifying type $A_{N-1}$ 6d ${cal N}{=}(2,0)$ supersymmetric CFT on a product manifold $M^4timesSigma^2=M^3timestilde{S}^1times S^1times{cal I}$ either over $S^1$ or over $tilde{S}^1$ leads to maximally supersymmetric 5d gauge theories on $M^4times{cal I}$ or on $M^3timesSigma^2$, respectively. Choosing the radii of $S^1$ and $tilde{S}^1$ inversely proportional to each other, these 5d gauge theories are dual to one another since their coupling constants $e^2$ and $tilde{e}^2$ are proportional to those radii respectively. We consider their non-Abelian but non-supersymmetric extensions, i.e. SU($N$) Yang-Mills theories on $M^4times{cal I}$ and on $M^3timesSigma^2$, where $M^4supset M^3=mathbb R_ttimes T_p^2$ with time $t$ and a punctured 2-torus, and ${cal I}subsetSigma^2$ is an interval. In the first case, shrinking ${cal I}$ to a point reduces to Yang-Mills theory or to the Skyrme model on $M^4$, depending on the method chosen for the low-energy reduction. In the second case, scaling down the metric on $M^3$ and employing the adiabatic method, we derive in the infrared limit a non-linear SU($N$) sigma model with a baby-Skyrme-type term on $Sigma^2$, which can be reduced further to $A_{N-1}$ Toda theory.
The geometry of the ${cal N} = 3$, SO(4)--invariant, AdS$_4$ solution of massive type IIA supergravity that uplifts from the ${cal N} = 3 $ vacuum of $D=4$ ${cal N} = 8$ dyonic ISO(7) supergravity is investigated. Firstly, a $D=4$, SO(4)--invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)--invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the ${cal N} = 3 $ AdS$_4$ solution in massive IIA and analyse its geometry. Locally, the internal $S^6$ geometry corresponds to a warped fibration of $S^2$ and a hemisphere of $S^4$. This can be regarded as a warped generalisation of the usual twistor fibration geometry. Finally, the triplet of Killing spinors corresponding to the ${cal N}=3$ solution are constructed and shown to obey the massive type IIA Killing spinor equations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
