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T-Duality Effects in Electrodynamics: The (2+1)-dimensional Case

Patricio Gaete, Piero Nicolini

TL;DR

The paper studies how T-duality affects gauge fields in $\left(2+1\right)$-dimensional electrodynamics using a nonlocal operator $\mathcal{O}$ controlled by a fundamental scale $l_0$. This yields a modified propagator and a gauge-invariant framework to compute the static intercharge potential. Results show a finite $V(r)$ at $r\to 0$ and a logarithmic large-$r$ behavior, with a dual-coordinate transformation $\rho = l_0^2/r$ highlighting a dual-regulation picture and fractal-like scaling captured by $\mathbb{D}$. The work suggests that $l_0$ can regulate divergences in low-dimensional gauge theories and may have relevance for condensed-matter systems exhibiting fractal or strange-metal features.

Abstract

We investigate the interplay between T-duality and (2+1)- dimensional electrodynamics, revealing a relationship between short and large length scales of the gauge potential. Our findings demonstrate that the electrostatic potential energy between static charges is no longer divergent at short distances in the presence of T-duality effects. It remains logarithmic at large distances, suggesting the possibility of a regulatory role for the T-duality scale \( l_0 \) in the space where the radial coordinate goes into its inverse. We also discuss the potential of T-duality to elucidate fractalization effects in physical systems, paving the way for future research on the implications for superconductors and condensed matter systems in general.

T-Duality Effects in Electrodynamics: The (2+1)-dimensional Case

TL;DR

The paper studies how T-duality affects gauge fields in -dimensional electrodynamics using a nonlocal operator controlled by a fundamental scale . This yields a modified propagator and a gauge-invariant framework to compute the static intercharge potential. Results show a finite at and a logarithmic large- behavior, with a dual-coordinate transformation highlighting a dual-regulation picture and fractal-like scaling captured by . The work suggests that can regulate divergences in low-dimensional gauge theories and may have relevance for condensed-matter systems exhibiting fractal or strange-metal features.

Abstract

We investigate the interplay between T-duality and (2+1)- dimensional electrodynamics, revealing a relationship between short and large length scales of the gauge potential. Our findings demonstrate that the electrostatic potential energy between static charges is no longer divergent at short distances in the presence of T-duality effects. It remains logarithmic at large distances, suggesting the possibility of a regulatory role for the T-duality scale in the space where the radial coordinate goes into its inverse. We also discuss the potential of T-duality to elucidate fractalization effects in physical systems, paving the way for future research on the implications for superconductors and condensed matter systems in general.
Paper Structure (5 sections, 33 equations, 1 figure)

This paper contains 5 sections, 33 equations, 1 figure.

Table of Contents

  1. Introduction
  2. T-Duality Effects in Electrodynamics
  3. Calculation of the (2+1)-D static potential
  4. Conclusions
  5. Gauge-Invariant Computation of Interaction Energy

Figures (1)

  • Figure 1: Shape of the modulus of the potential, $|V(r)|$ in units of $\frac{2Q^2}{\pi}$ -- see (\ref{['eq:finalresult']}). The dashed line represents the Coulomb potential.