Abstract
We derive the Toverline{T} -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the Toverline{T} -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the Toverline{T} -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the Toverline{T} -deformation decreases the contribution of the Boltzmann entropy.
Highlights
A further step in this direction was made in [5, 6], where a path integral formulation of the T T -deformed theory was put forward: it was proven in [5, 6] that the deformation of a given quantum field theory by the T T operator is equivalent to coupling the undeformed theory to flat space Jackiw-Teitelboim (JT) gravity
For the U(N ) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons
A simple proposal for the T T -deformation of Yang-Mills theory on a Riemann surface was advocated by [37]: due to the simple form of the evolution of the two-dimensional Yang-Mills Hamiltonian with the deformation parameter τ, the T T -deformed version of the theory amounts to replacing the quadratic Casimir that appears in the usual heat kernel expansion of the partition function according to
Summary
Consider the partition function of a gauge theory T with compact connected gauge group G on a Riemann surface Σ which is described by the insertion of a non-local operator O(Φ) in the path integral of a two-dimensional topological quantum field theory: ZT [Σ] =. In the present setting, we argue that, since the underlying theory is topological, for suitable insertions O(Φ) we can define the T T -deformation on flat space, and put the theory on a curved manifold Σ. We should be able, at least in principle, to glue the pieces together, at the price of solving the gluing theory [48], which will be a quantum mechanics deformed by the effect of the change of variables on the boundary modes
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