arXiv subjects

Miguel Tierz

Publications and source records attributed to Miguel Tierz.

57 records · Page 4Linked to original sources

arXiv2005

Quantum group symmetry and discrete scale invariance: Spectral aspects

We study analytical aspects of a generic q-deformation with q real, by relating it with discrete scale invariance. We show how models of conformal quantum mechanics, in the strong coupling regime and after regularization, are also discrete scale invariant. We discuss the consequences of their distinctive spectra, characterized by functional behavior. The role of log-periodic behavior and q-periodic functions is examined, and we show how q-deformed zeta functions, characterized by complex poles, appear. As an application, we discuss one-loop effects in discretely self-similar space-times.

hep-th↗

arXiv2004

Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills

We point out a precise connection between Brownian motion, Chern-Simons theory on S^3, and 2d Yang-Mills theory on the cylinder. The probability of reunion for N vicious walkers on a line gives the partition function of Chern-Simons theory on S^3 with gauge group U(N). The probability of starting with an equal-spacing condition and ending up with a generic configuration of movers gives the expectation value of the unknot. The probability with arbitrary initial and final states corresponds to the expectation value of the Hopf link. We find that the matrix model calculation of the partition function is nothing but the additivity law of probabilities. We establish a correspondence between quantities in Brownian motion and the modular S- and T-matrices of the WZW model at finite k and N. Brownian motion probabilitites in the affine chamber of a Lie group are shown to be related to the partition function of 2d Yang-Mills on the cylinder. Finally, the random-turns model of discrete random walks is related to Wilson's plaquette model of 2d QCD, and the latter provides an exact two-dimensional analog of the melting crystal corner. Brownian motion provides a useful unifying framework for understanding various low-dimensional gauge theories.

hep-th↗

arXiv2004

Soft matrix models and Chern-Simons partition functions

We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. We mainly rely on simple considerations based on orthogonal polynomials and the moment problem. In addition, some of these models are equivalent, by a simple mapping, to matrix models that appear in Chern-Simons theory. The models can be solved with q deformed orthogonal polynomials (Stieltjes-Wigert polynomials), and the deformation parameter turns out to be the usual $q$ parameter in Chern-Simons theory. In this way, we give a matrix model computation of the Chern-Simons partition function on $S^{3}$ and show that there are infinitely many matrix models with this partition function.

hep-th↗