arXiv subjects

E. T. Tomboulis

Publications and source records attributed to E. T. Tomboulis.

At least 37 records · Page 2Linked to original sources

arXiv2010

Can Lorentz-breaking fermionic condensates form in large N strongly-coupled Lattice Gauge Theories?

The possibility of Lorentz symmetry breaking (LSB) has attracted considerable attention in recent years for a variety of reasons, including the attractive prospect of the graviton as a Goldstone boson. Though a number of effective field theory analyses of such phenomena have recently been given it remains an open question whether they can take place in an underlying UV complete theory. Here we consider the question of LSB in large N lattice gauge theories in the strong coupling limit. We apply techniques that have previously been used to correctly predict the formation of chiral symmetry breaking condensates in this limit. Generalizing such methods to other composite operators we find that certain LSB condensates can indeed form. In addition, the interesting possibility arises of condensates that 'lock' internal with external symmetries.

hep-lat↗

arXiv2007

Reply to arXiv:0711.4930[hep-th] by Ito and Seiler

In a recent note (arXiv:0711.4930[hep-th]) Ito and Seiler claim that there is a 'missing link' in the derivation in arXiv:0707.2179[hep-th] by the present author; namely, that no proof of a certain inequality used there is given at weak coupling. Here it is pointed out that in fact no such missing link is present. The argument in 0707.2179 is, among other things, specifically constructed so that the inequality in question is invoked {\it only} at strong coupling, where it is easily proven. Underlying the mangling of the argument in 0707.2179 by Ito and Seiler are their incorrect statements concerning the dependence of the potential-moving decimation procedures used in 0707.2179 on space-time dimensionality and other decimation parameters.

hep-th↗

arXiv2007

Deriving confinement via RG decimations

We present the general framework and building blocks of a recent derivation of the fact that the SU(2) LGT is in a confining phase for all values of the coupling $0 < β< \infty$, for space-time dimension $d \leq 4$. The method employs approximate but explicitly computable RG decimations that are shown to constrain the exact partition function and order parameters from above and below, and flow from the weak to the strong coupling regime without encountering a fixed point.

hep-lat↗

arXiv2007

Improved actions and lattice coarsening effects in MCRG studies in SU(2) LGT

We study decimation procedures and effective (improved) actions in the framework of Monte Carlo Renormalization Group (MCRG). Particular attention is paid to matching the form of the effective action to the decimation procedure parameters. Using the static quark-antiquark potential in SU(2) LGT we probe different distance scales and find that an effective action containing multiple group representations is capable of reproducing long distance physics well. In particular, appropriate matching results in the practical elimination of the coarsening/fining effect of the lattice spacing under decimation. The short distance regime of the effective theory is also studied. We next carry out studies of effective actions involving both multiple representations and loops beyond the single plaquette towards determining an improved action good over a wide length scale regime.

hep-lat↗

arXiv2007

Confinement for all values of the coupling in four-dimensional SU(2) gauge theory

A derivation is given from first principles of the fact that the SU(2) gauge theory is in a confining phase for all values of the coupling $0 < g < \infty$ defined at lattice spacing (UV regulator) $a$, and space-time dimension $d \leq 4$. The strategy is to employ approximate RG decimation transformations of the potential moving type which give both upper and lower bounds on the partition function at each successive decimation step. By interpolation between these bounds an exact representation of the partition function is obtained on progressively coarser lattices. In the same manner, one obtains a representation of the partition function in the presence of external center flux. Under successive decimations the flow of the effective action in these representations is constrained by that in the upper and lower bounds which are easily explicitly computable. Confining behavior for the vortex free energy order parameter (ratio of partition functions with and without external flux), hence `area law' for the Wilson loop, is the result for any initial coupling. Keeping the string tension fixed determines the dependence $g(a)$, which is such that $g(a) \to 0$ for $a \to 0$.

hep-th↗

arXiv2007

String tension and removal of lattice coarsening effects in Monte Carlo Renormalization Group

We study the computation of the static quark potential under decimations in the Monte Carlo Renormalization Group (MCRG). Employing a multi-representation plaquette action, we find that fine-tuning the decimation prescription so that the MCRG equilibrium self-consistency condition is satisfied produces dramatic improvement at large distances. In particular, lattice coarsening (change of effective lattice spacing on action-generated lattices after decimation) is nearly eliminated. Failure to correctly tune the decimation, on the other hand, produces large coarsening effects, of order 50% or more, consistent with those seen in previous studies. We also study rotational invariance restoration at short distances, where no particular improvement is seen for this action.

hep-lat↗

arXiv2007

Improving the improved action

We investigate the construction of improved actions by the Monte Carlo Renormalization Group method in the context of SU(2) gauge theory utilizing different decimation procedures and effective actions. We demonstrate that the basic self-consistency requirement for correct application of MCRG, i.e. that the decimated configurations are equilibrium configurations of the adopted form of the effective action, can only be achieved by careful fine-tuning of the choice of decimation prescription and/or action.

hep-lat↗

arXiv2007

Renormalization Group Therapy

We point out a general problem with the procedures commonly used to obtain improved actions from MCRG decimated configurations. Straightforward measurement of the couplings from the decimated configurations, by one of the known methods, can result into actions that do not correctly reproduce the physics on the undecimated lattice. This is because the decimated configurations are generally not representative of the equilibrium configurations of the assumed form of the effective action at the measured couplings. Curing this involves fine-tuning of the chosen MCRG decimation procedure, which is also dependent on the form assumed for the effective action. We illustrate this in decimation studies of the SU(2) LGT using Swendsen and Double Smeared Blocking decimation procedures. A single-plaquette improved action involving five group representations and free of this pathology is given.

hep-lat↗

arXiv2006

RG decimation study of SU(2) gauge theory

We report on numerical studies of RG decimations in SU(2) gauge theory. We study in particular a class of plaquette actions involving sums of group representations. We measure a number of observables representative of different length scales in order to investigate the transformation of the system under different choices of spin blocking, and examine the flow of the effective action couplings. A need for a projection to some class of effective actions on the configurations resulting from the adopted numerical decimation procedures is demonstrated. A numerical decimation procedure resulting in the effective single plaquette Lagrangian tailored to reproduce different medium/large scale physics is devised.

hep-lat↗

arXiv2005

Deconfinement transition dynamics and early thermalization in QGP

We perform SU(3) Lattice Gauge Theory simulations of the deconfinement transition attempting to mimic conditions encountered in heavy ion collisions. Specifically, we perform a sudden temperature quench across the deconfinement temperature, and follow the response of the system in successive simulation sweeps under spatial lattice expansion and temperature fall-off. In measurements of the Polyakov loop and structure functions a robust strong signal of global instability response is observed through the exponential growth of low momentum modes. Development of these long range modes isotropizes the system which reaches thermalization shortly afterwards, and enters a stage of quasi-equilibrium expansion and cooling till its return to the confinement phase. The time scale characterizing full growth of the long range modes is largely unaffected by the conditions of spatial expansion and temperature variation in the system, and is much shorter than the scale set by the interval to return to the confinement phase. The wide separation of these two scales is such that it naturally results in isotropization times well inside 1 fm/c.

hep-ph↗

arXiv2005

RG decimation-based approach to confinement and computation on coarser lattices

A systematic procedure is presented for connecting short to long scales in LGT. Approximate decimations are used which can provide both upper and lower bounds on the partition function. Its exact value is then obtained by interpolation between the bounds. By iterating the procedure representations of the partition function as well as other physical quantities can be obtained on progressively coarser lattices. For SU(2) IR flow into the confining strong coupling regime results for any initial $β$.

hep-lat↗

arXiv2004

RG Decimations and Confinement

We outline the steps in a derivation of the statement that the SU(2) gauge theory is in a confining phase for all values of the coupling, $0 < β<\infty$, defined at lattice spacing a. The approach employed is to obtain both upper and lower bounds for the partition function and the `twisted' partition function in terms of approximate decimation transformations. The behavior of the exact quantities is thus constrained by that of the easily computable bounding decimations.

hep-lat↗

arXiv2003

Connecting short to long scales in the confining vacuum

We study approximate decimations in SU(N) LGT that connect the short to long distance regimes. Simple `bond-moving' decimations turn out to provide both upper and lower bounds on the exact partition function. This leads to a representation of the exact partition function in terms of successive decimations whose effective couplings flows are related to those of the easily computable bond-moving decimations. The implications for a derivation of confinement from first principles are discussed.

hep-lat↗

arXiv2003

From short to long scales in the QCD vacuum

We study approximate decimations in SU(N) LGT that connect the short to long distance regimes, and provide both upper and lower bounds on the exact partition function. This leads to a representation of the exact partition function in terms of successive decimations. The implications for a derivation of confinement from first principles are discussed.

hep-lat↗

arXiv2002

Loop inequalities and confinement

We consider correlation inequalities that follow from the well-known loop equations of LGT, and their analogues in spin systems. They provide a way of bounding long range by short or intermediate range correlations. In several cases the method easily reproduces results that otherwise require considerable effort to obtain. In particular, in the case of the 2-dimensional O(N) spin model, where large N analytical results are available, the absence of a phase transition and the exponential decay of correlations for all $β$ is easily demonstrated. We report on the possible application of this technique to the analogous 4-dimensional problem of area law for the Wilson loop in LGT at large $β$.

hep-lat↗

arXiv2002

Photons and Gravitons as Goldstone Bosons, and the Cosmological Constant

We reexamine a scenario in which photons and gravitons arise as Goldstone bosons associated with the spontaneous breaking of Lorentz invariance. We study the emergence of Lorentz invariant low energy physics in an effective field theory framework, with non-Lorentz invariant effects arising from radiative corrections and higher order interactions. Spontaneous breaking of the Lorentz group also leads to additional exotic but weakly coupled Goldstone bosons, whose dispersion relations we compute. The usual cosmological constant problem is absent in this context: being a Goldstone boson, the graviton can never develop a potential, and the existence of a flat spacetime solution to the field equations is guaranteed.

hep-th↗

arXiv2001

Vortex waistlines and long range fluctuations

We examine the manner in which a linear potential results from fluctuations due to vortices linked with the Wilson loop. Our discussion is based on exact relations and inequalities between the Wilson loop and the vortex and electric flux order parameters. We show that, contrary to the customary naive picture, only vortex fluctuations of thickness of the order of the spatial linear size of the loop are capable of producing a strictly linear potential. An effective theory of these long range fluctuations emerges naturally in the form of a strongly coupled Z(N) lattice gauge theory. We also point out that dynamical fermions introduced in this medium undergo chiral symmetry breaking.

hep-lat↗

arXiv2001

Vortex waistlines and vortex gas

We investigate the manner in which a linear potential arises from fluctuations due to vortices linked with the Wilson loop. In particular, the customary naive picture is critically reexamined.

hep-lat↗