SISSA PreprintsThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2020-05-29T20:12:00Z2020-05-29T20:12:00ZSuperconformal indices at large N and the entropy of AdS5 × SE5 black holesBenini, FrancescoColombo, EdoardoSoltani, SamanZaffaroni, AlbertoZhang, Ziruohttp://preprints.sissa.it:8180/xmlui/handle/1963/353532020-05-28T23:20:29Z2020-05-01T00:00:00ZSuperconformal indices at large N and the entropy of AdS5 × SE5 black holes
Benini, Francesco; Colombo, Edoardo; Soltani, Saman; Zaffaroni, Alberto; Zhang, Ziruo
The large N limit of the four-dimensional superconformal index was computed and successfully compared to the entropy of a class of AdS5 black holes only in the particular case of equal angular momenta. Using the Bethe Ansatz formulation, we compute the index at large N with arbitrary chemical potentials for all charges and angular momenta, for general N = 1 four-dimensional conformal theories with a holographic dual. We con-jecture and bring some evidence that a particular universal contribution to the sum over Bethe vacua dominates the index at large N. For N = 4 SYM, this contribution correctly leads to the entropy of BPS Kerr-Newman black holes in AdS5 × S5 for arbitrary values of the conserved charges, thus completing the microscopic derivation of their microstates. We also consider theories dual to AdS5 × SE5, where SE5 is a Sasaki-Einstein manifold. We ﬁrst check our results against the so-called universal black hole. We then explicitly construct the near-horizon geometry of BPS Kerr-Newman black holes in AdS5 × T 1,1, charged under the baryonic symmetry of the conifold theory and with equal angular mo-menta. We compute the entropy of these black holes using the attractor mechanism and we ﬁnd complete agreement with the ﬁeld theory predictions.
SISSA, Via Bonomea 265, 34136 Trieste, Italy, INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy, ICTP, Strada Costiera 11, 34151 Trieste, Italy, Dipartimento di Fisica, Universit`a di Milano-Bicocca, I-20126 Milano, Italy, INFN, Sezione di Milano-Bicocca, I-20126 Milano, Italy
2020-05-01T00:00:00ZForward untangling and applications to the uniqueness problem for the continuity equationBianchini, StefanoBonicatto, Paolohttp://preprints.sissa.it:8180/xmlui/handle/1963/353522020-05-22T23:20:34Z2020-05-01T00:00:00ZForward untangling and applications to the uniqueness problem for the continuity equation
Bianchini, Stefano; Bonicatto, Paolo
Contents:
Introduction: Synopsis of the paper Acknowledgements.
1. Notation.
2. Preliminaries on Lagrangian representations, proper sets and Optimal Transport.
2.1. Lagrangian representations.
2.2. Proper sets.
2.3. Optimal transport and duality.
3. Optimal transport and duality.
4. The global theory of forward untangling.
4.1. Subadditivity of untangling functional.
5. Uniqueness by forward untangling.
5.1. Decomposition and disintegration.
5.2. Composition rule.
6. Monotone vector ﬁelds.
References.
2020-05-01T00:00:00ZOn the sticky particle solutions to the multi-dimensional pressureless Euler equationsBianchini, StefanoDaneri, Sarahttp://preprints.sissa.it:8180/xmlui/handle/1963/353512020-05-22T23:20:31Z2020-05-01T00:00:00ZOn the sticky particle solutions to the multi-dimensional pressureless Euler equations
Bianchini, Stefano; Daneri, Sara
In this paper we consider the multi-dimensional pressureless Euler system and we tackle the problem of existence and uniqueness of sticky particle solutions for general measure-type initial data. Although explicit counterexamples to both existence and uniqueness are known since [5], the problem of whether one can still ﬁnd sticky particle solutions for a large set of data and of how one can select them was up to our knowledge still completely open. In this paper we prove that for a comeager set of initial data in the weak topology the pressureless Euler system admits a unique sticky particle solution given by a free ﬂow where trajectories are disjoint straight lines. Indeed, such an existence and uniqueness result holds for a broader class of solutions de-creasing their kinetic energy, which we call dissipative solutions, and which turns out to be the compact weak closure of the classical sticky particle solutions. Therefore any scheme for which the energy is l.s.c. and is dissipated will converge, for a comeager set of data, to our solution, i.e. the free ﬂow.
2020-05-01T00:00:00ZNon-well-ordered lower and upper solutions for semilinear systems of PDEsFonda, AlessandroKlun, GiulianoSfecci, Andreahttp://preprints.sissa.it:8180/xmlui/handle/1963/353502020-05-04T23:20:29Z2020-05-01T00:00:00ZNon-well-ordered lower and upper solutions for semilinear systems of PDEs
Fonda, Alessandro; Klun, Giuliano; Sfecci, Andrea
We prove existence results for systems of boundary value problems involving elliptic second order diﬀerential operators. The as-sumptions involve lower and upper solutions, which may be either well-ordered, or not at all. The results are stated in an abstract framework, and can be translated also for systems of parabolic type.
2020-05-01T00:00:00Z