arXiv subjects

Javier Mas

Publications and source records attributed to Javier Mas.

43 records · Page 3Linked to original sources

arXiv1999

N=2 supersymmetric Yang-Mills theories and Whitham integrable hierarchies

We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole instanton expansion of the low-energy effective prepotential; (ii) We interpret the slow times of the hierarchy as additional couplings and promote them to spurion superfields that softly break N=2 supersymmetry down to N=0 through deformations associated to higher Casimir operators of the gauge group; (iii) We show that the Seiberg-Witten-Whitham equations provide a set of non-trivial constraints on the form of the strong coupling expansion in the vicinity of the maximal singularities. We use them to check a proposal that we make for the value of the off-diagonal couplings at those points of the moduli space.

hep-th↗

arXiv1999

Strong coupling expansion and Seiberg-Witten-Whitham equations

We study the Seiberg-Witten-Whitham equations in the strong coupling regime of the N=2 super Yang-Mills theory in the vicinity of the maximal singularities. In the case of SU(2) the Seiberg-Witten-Whitham equations fix completely the strong coupling expansion. For higher rank SU(N) they provide a set of non-trivial constraints on the form of this expansion. As an example, we study the off-diagonal couplings at the maximal point for which we propose an ansatz that fulfills all the equations.

hep-th↗

arXiv1998

Whitham Hierarchies, Instanton Corrections and Soft Supersymmetry Breaking in N=2 SU(N) Super Yang-Mills Theory

We study N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy. We develop a new recursive method to compute the whole instanton expansion of the prepotential using the theta function associated to the root lattice of the group. Explicit results for the one and two-instanton corrections in SU(N) are presented. Interpreting the slow times of the hierarchy as additional couplings, we show how they can be promoted to spurion superfields that softly break N=2 supersymmetry down to N=0. This provides a family of nonsupersymmetric deformations of the theory, associated to higher Casimir operators of the gauge group. The SU(3) theory is analyzed in some detail.

hep-th↗

arXiv1996

The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra

In this paper we continue with the program to explore the topography of the space of W-type algebras. In the present case, the starting point is the work of Khesin, Lyubashenko and Roger on the algebra of q-deformed pseudodifferential symbols and their associated integrable hierarchies. The analysis goes on by studying the associated hamiltonian structures for which compact expressions are found. The fundamental Poisson brackets yield q-deformations of W_{KP} and related W-type algebras which, in specific cases, coincide with the ones constructed by Frenkel and Reshetikhin. The construction underlies a continuous correspondence between the hamiltonian structures of the Toda lattice and the KP hierarchies.

q-alg↗

arXiv1995

The Constrained KP Hierarchy and the Generalised Miura Transformation

Recently much attention has been paid to the restriction of KP to the submanifold of operators which can be represented as a ratio of two purely differential operators L=AB^{-1}. Whereas most of the aspects concerning this reduced hierarchy, like the Lax flows and the Hamiltonians, are by now well understood, there still lacks a clear and conclusive statement about the associated Poisson structure. We fill this gap by placing the problem in a more general framework and then showing how the required result follows from an interesting property of the second Gelfand-Dickey brackets under multiplication and inversion of Lax operators. As a byproduct we give an elegant and simple proof of the generalised Kupershmidt-Wilson theorem.

q-alg↗

arXiv1994

Centrally Extended W_{1+\infty} and the KP Hierarchy

It is well known that the centerless W_{1+\infty} algebra provides a hamiltonian structure for the KP hierarchy. In this letter we address the question whether the centerful version plays a similar rôle in any related integrable system. We find that, surprisingly enough, the centrally extended W_{1+\infty} algebra yields yet another Poisson structure for the same standard KP hierarchy. This is proven by explicit construction of the infinitely many new hamiltonians in closed form.

hep-th↗

arXiv1993

Diffeomorphisms from higher dimensional W-algebras

Classical W-algebras in higher dimensions have been recently constructed. In this letter we show that there is a finitely generated subalgebra which is isomorphic to the algebra of local diffeomorphisms in D dimensions. Moreover, there is a tower of infinitely many fields transforming under this subalgebra as symmetric tensorial one-densities. We also unravel a structure isomorphic to the Schouten symmetric bracket, providing a natural generalization of w_\infty in higher dimensions.

hep-th↗