Margarita Garcia Perez

Topology of the SU (2) vacuum: a lattice study using improved cooling

We study the topological structure of the SU(2) vacuum at zero temperature: topological susceptibility, size, shape and distance distributions of the instantons. We use a cooling algorithm based on an improved action with scale invariant instanton solutions. This algorithm needs no monitoring or calibration, has an inherent cut off for dislocations and leaves unchanged instantons at physical scales. The physical relevance of our results is checked by studying the scaling and finite volume dependence. We obtain a susceptibility of (200(15) MeV)4. The instanton size distribution is peaked around 0.43 fm, and the distance distribution indicates a homogeneous, random spatial structure.

Magnetic field production during preheating at the electroweak scale.

We study the generation of magnetic fields during preheating within a scenario of hybrid inflation at the electroweak scale. We find that the nonperturbative and strongly out-of-equilibrium process of generation of magnetic fields with a nontrivial helicity occurs along the lines predicted by Vachaspati many years ago. The magnitude (rho_{B}/rho_{EW} approximately 10{-2}) and correlation length of these helical magnetic fields grow linearly with time during preheating and are consistent with the possibility that these seeds gave rise to the microgauss fields observed today in galaxies and clusters of galaxies.

Chern-Simons production during preheating in hybrid inflation models

PACS numbers: 98.80.Cq.-- 28 pages, 15 figures, ReVTeX.-- Submitted on 30 Apr 2003 (v1), last revised 16 Sep 2003 (this version, v2).-- With minor corrections, version to appear in Phys. Rev. D.

Weyl-Dirac zero mode for calorons

In this paper, we give the exact expression for the SU(2) fermion zero mode in the field of the infinite volume caloron with a nontrivial holonomy and unit charge. Study of the gauge field configurations had, somewhat surprisingly, revealed that at nontrivial holonomy calorons have two Bogomol’nyi-Prasad-Sommerfield ~BPS! monopoles @N for SU(N)# as their constituents @1,2,3#. For the HarringtonShepard @4# solution with trivial holonomy, this is hidden because one of the constituents is massless ~it can be removed by a singular gauge transformation to show that the caloron for a large scale parameter becomes a single BPS monopole @5#!. We find that, for calorons with wellseparated constituents, the fermion zero mode is entirely supported on one of them. In itself it is not surprising that the zero mode is correlated to the monopole constituents. Independently, this observation was recently also made for gluino zero modes in the context of supersymmetric gauge theories @6#. Gluinos are in the adjoint representation of the gauge group, such that there are four zero modes that can be split in pairs associated with each of the two constituents @6#. However, for the Dirac fermion, there is only one zero mode. To understand the ‘‘affinity’’ of the zero mode to only one of the two monopoles, we will analyze in some detail what distinguishes them. Calorons are characterized by the ~fixed! holonomy @1,7#. In the gauge in which Am(x) is periodic, this holonomy is given by

Primordial magnetic fields from preheating at the electroweak scale

We analyze the generation of helical magnetic fields during preheating in a model of low-scale electroweak (EW) hybrid inflation. We show how the inhomogeneities in the Higgs field, resulting from tachyonic preheating after inflation, seed the magnetic fields in a way analogous to that predicted by Vachaspati and Cornwall in the context of the EW symmetry breaking. At this stage, the helical nature of the generated magnetic fields is linked to the non-trivial winding of the Higgs-field. We analyze non-perturbatively the evolution of these helical seeds through the highly non-linear stages of symmetry breaking (SB) and beyond. Electroweak SB occurs via the nucleation and growth of Higgs bubbles which squeeze the magnetic fields into string-like structures. The W-boson charge density clusters in lumps around the magnetic strings. After symmetry breaking, a detailed analysis of the magnetic field Fourier spectrum shows two well differentiated components: a UV radiation tail at a temperature T ~ 0.23 mH, slowly growing with time, and an IR peak associated to the helical magnetic fields, which seems to follow inverse cascade. The system enters a regime in which we observe that both the amplitude (ρB/ρEW ~ 10−2) and the correlation length of the magnetic field grow linearly with time. During this stage of evolution we also observe a power-law growth in the helical susceptibility. These properties support the possibility that our scenario could provide the seeds eventually evolving into the microgauss fields observed today in galaxies and clusters of galaxies.

Calorons on the lattice - a new perspective

We discuss the manifestation of instanton and monopole solutions on a periodic lattice at finite temperature and their relation to the infinite volume analytic caloron solutions with asymptotic non-trivial Polyakov loops. As a tool we use improved cooling and twisted boundary conditions. Typically we find 2Q lumps for topological charge Q. These lumps are BPS monopoles.

Cooling, physical scales and topology

Abstract We develop a cooling method controlled by a physical cooling radius that defines a scale below which fluctuations are smoothed out while leaving physics unchanged at all larger scales. We apply this method to study topological properties of lattice gauge theories, in particular the behaviour of instantons, dislocations and instanton-anti-instanton pairs. Monte Carlo results for the SU (2) topology are presented. We find that the method provides a means to prevent instantonanti-instanton annihilation under cooling. While the instanton sizes are largely independent from the smoothing scale, the density and pair separations are determined by the particular choice made for this quantity. We discuss the questions this raises for the “physicality” of these concepts.

Spatial volume dependence for 2+1 dimensional SU(N) Yang-Mills theory

A bstractWe study the 2+1 dimensional SU(N) Yang-Mills theory on a finite two-torus with twisted boundary conditions. Our goal is to study the interplay between the rank of the group N , the length of the torus L and the ZN magnetic flux. After presenting the classical and quantum formalism, we analyze the spectrum of the theory using perturbation theory to one-loop and using Monte Carlo techniques on the lattice. In perturbation theory, results to all orders depend on the combination x = λN L and an angle

Properties of hadron screening masses at small baryonic density

\widetilde{\theta }

Nahm dualities on the torus - a synthesis

defined in terms of the magnetic flux (λ is ‘t Hooft coupling). Thus, fixing the angle, the system exhibits a form of volume independence (N L dependence). The numerical results interpolate between our perturbative calculations and the confinement regime. They are consistent with x-scaling and provide interesting information about the k-string spectrum and effective string theories. The occurrence of tachyonic instabilities is also analysed. They seem to be avoidable in the large N limit with a suitable scaling of the magnetic flux.