Estanislao Herscovich

Black holes in Einstein–Gauss–Bonnet gravity with a string cloud background

Abstract We obtain a black hole solution in the Einstein–Gauss–Bonnet theory for the string cloud model in a five-dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature T H , the specific heat C , the entropy S , and the Helmholtz free energy F of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Walds entropy is considered for the string cloud source. We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking–Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss–Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background.

Winding strings in AdS3

Correlation functions of one-unit spectral flowed states in string theory on AdS3 are considered. We present the modified Knizhnik-Zamolodchikov and null vector equations to be satisfied by amplitudes containing states in winding sector one and study their solution corresponding to the four point function including one w = 1 field. We compute the three point function involving two one-unit spectral flowed operators and find expressions for amplitudes of three w = 1 states satisfying certain particular relations among the spins of the fields. Several consistency checks are performed.

Hochschild and cyclic homology of Yang-Mills algebras

Abstract The aim of this article is to present a detailed algebraic computation of the Hochschild and cyclic homology groups of the Yang–Mills algebras YM(n) (n ∈ ℕ≧2) defined by A. Connes and M. Dubois-Violette in [8], continuing thus the study of these algebras that we have initiated in [17]. The computation involves the use of a spectral sequence associated to the natural filtration on the universal enveloping algebra YM(n) provided by a Lie ideal 𝔱𝔶𝔪(n) in 𝔶𝔪(n) which is free as Lie algebra. As a corollary, we describe the Lie structure of the first Hochschild cohomology group.

PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras

In this article we establish an explicit link between the classical theory of deformations \`a la Gerstenhaber -- and a fortiori with the Hochschild cohomology-- and (weak) PBW-deformations of homogeneous algebras. Our point of view is of cohomological nature. As a consequence, we recover a theorem by R. Berger and V. Ginzburg, which gives a precise condition for a filtered algebra to satisfy the so-called PBW property, under certain assumptions.

Representations of Super Yang-Mills Algebras

We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149–158, 2002), and in fact they appear as a “background independent” formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras

Noncommutative Valuation of Options

{{\rm {Cliff}}_{q}(k) \otimes A_{p}(k)}

Hochschild (co)homology and Koszul duality

, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.

Hochschild¿Mitchell cohomology and Galois extensions

Our objective is to show a possibly interesting structure of homotopic nature appearing in persistent (co)homology. Assuming that the filtration of a simplicial set embedded in