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

We study a T T ¯ -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 T T ¯ -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.