Burgers equation vs. large N limit in TT¯-deformed O(N) vector model

Abstract

We study a TT¯-deformed O(N) vector model, which is classically equivalent to the Nambu-Goto action with static gauge. The thermal free energy density can be computed exactly by using the Burgers equation as a special property of TT¯-deformation. The resulting expression is valid for an arbitrary value of N. One may consider a large N limit while preserving this expression. We try to derive this result in the field-theoretical approach directly by employing the large N limit. As a result, the leading contribution coincides with the exact one. That is, the 1/N corrections are canceled out through a non-trivial mechanism.