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Robert Lohmayer

Publications and source records attributed to Robert Lohmayer.

30 records · Page 2Linked to original sources
arXiv2013

Weak-coupling analysis of the single-site large-N gauge theory coupled to adjoint fermions

We consider the leading-order expression at weak-coupling for a single-site large-N gauge theory coupled to adjoint fermions. We study the case of overlap and wilson fermions. We extend the theory to real values of the number of fermion flavors and restrict ourselves to asymptotically free theories. Using a four-dimensional density function for the distribution of the eigenvalues of the link variables, we show that it is possible to recover the infinite-volume continuum limit for a certain range of fermion flavors if we use fermions with a bare mass of zero. Our use of the four-dimensional density function is supported by a direct analysis of the lattice action.

hep-lat↗
arXiv2012

Large-N string tension from rectangular Wilson loops

In pure SU(N) gauge theory in four dimensions, we determine the string tension at large N from smeared rectangular Wilson loops on the lattice. We learn how well loops of sizes barely on the strong-coupling side of the large-N transition in their eigenvalue distribution can be described by effective string theory.

hep-lat↗
arXiv2012

Rectangular Wilson Loops at Large N

This work is about pure Yang-Mills theory in four Euclidean dimensions with gauge group SU(N). We study rectangular smeared Wilson loops on the lattice at large N and relatively close to the large-N transition point in their eigenvalue density. We show that the string tension can be extracted from these loops but their dependence on shape differs from the asymptotic prediction of effective string theory.

hep-lat↗
arXiv2011

Numerical study of large-N phase transition of smeared Wilson loops in 4D pure YM theory

In Euclidean four-dimensional SU(N) pure gauge theory, eigenvalue distributions of Wilson loop parallel transport matrices around closed spacetime curves show non-analytic behavior (a 'large-N phase transition') at a critical size of the curve. We focus mainly on an observable composed of traces of the Wilson loop operator in all totally antisymmetric representations, which is regularized with the help of smearing. By studying sequences of square Wilson loops on a hypercubic lattice with standard Wilson action, it is shown that this observable has a nontrivial continuum limit as a function of the physical size of the loop. We furthermore present (preliminary) numerical results confirming that, for large N, the N dependence in the critical regime is governed by the universal exponents 1/2 and 3/4 as expected (Burgers universality).

hep-lat↗
arXiv2011

Continuous smearing of Wilson Loops

Continuum smearing was introduced in section 4.1 of JHEP03, 064 (2006) as a meaningful continuum analogue of the well known set of lattice techniques by the same name. Here we apply continuous smearing in continuous space-time to Wilson loops in order to clarify what it does in the context of field theory and also in the context of the loop calculus of the Makeenko-Migdal equation.

hep-lat↗
arXiv2009

Eigenvalue density of Wilson loops in 2D SU(N) YM at large N

The eigenvalue density of a Wilson loop matrix W associated with a simple loop in two-dimensional Euclidean SU(N) Yang-Mills theory undergoes a phase transition at a critical size in the infinite-N limit. The averages of 1/det(z-W) and det(1+uW)/(1-vW) at finite N lead to two different smoothed out expressions. It is shown by a saddle-point analysis that both functions tend to the known singular result at infinite N.

hep-th↗
arXiv2009

Wilson loops at finite N in 2D

Some exact expressions for non-selfintersecting Wilson loops in Yang Mills theory on the infinite plane are reviewed.

hep-lat↗
arXiv2009

Eigenvalue density of Wilson loops in 2D SU(N) YM

In 1981 Durhuus and Olesen (DO) showed that at infinite N the eigenvalue density of a Wilson loop matrix W associated with a simple loop in two-dimensional Euclidean SU(N) Yang-Mills theory undergoes a phase transition at a critical size. The averages of det(z-W), 1/det(z-W), and det(1+uW)/(1-vW) at finite N lead to three different smoothed out expressions, all tending to the DO singular result at infinite N. These smooth extensions are obtained and compared to each other.

hep-lat↗
arXiv2008

Possible large-N transitions for complex Wilson loop matrices

It is shown that a very simple multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a non-perturbative regime at a point where the smoothness of some quantities breaks down. A generic complex Wilson loop matrix in a field theory admitting a 't Hooft planar limit could display a phase transition in that limit as nonlinear effects become dominating over linear ones.

hep-th↗
arXiv2006

Entangled three-qubit states without concurrence and three-tangle

We provide a complete analysis of mixed three-qubit states composed of a GHZ state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this ``monogamy'' can be lifted for mixed states by virtue of vanishing tangle measures.

quant-ph↗