Effective strings in QED3

A bstract Effective string theory describes the physics of long confining strings in theories, like Yang-Mills theory, where the mass gap $$ {M}_{\textrm{gap}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>gap</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> is of the same order as the string tension T . In 2 + 1 dimensions, there is a class of confining theories, including massive QED 3 as first analyzed by Polyakov, for which $$ {M}_{\textrm{gap}}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>M</mml:mi> <mml:mi>gap</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> ≪ T . These theories are weakly coupled at low energies of order M gap , and may be analyzed perturbatively. In this paper, we analyze the physics of strings in such theories, focusing on QED 3 , at energies of order M gap (but still well below $$ \sqrt{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mi>T</mml:mi> </mml:msqrt> </mml:math> ). We argue that the width of the string in these theories should be of order 1/ M gap independently of its length, as long as the string is not exponentially long. We also compute at leading order in perturbation theory the ground state energy of a confining string on a circle, and the scattering of Nambu-Goldstone bosons on the string worldsheet.