A Symplectic Structure for String Theory on Integrable Backgrounds
نویسنده
چکیده
We define regularised Poisson brackets for the monodromy matrix of classical string theory on R × S 3. The ambiguities associated with Non-Ultra Locality are resolved using the symmetrisation prescription of Maillet. The resulting brackets lead to an infinite tower of Poisson-commuting conserved charges as expected in an integrable system. The brackets are also used to obtain the correct symplectic structure on the moduli space of finite-gap solutions and to define the corresponding action-angle variables. The canonically-normalised action variables are the filling fractions associated with each cut in the finite-gap construction. Our results are relevant for the leading-order semiclassical quantisation of string theory on AdS 5 × S 5 and lead to integer-valued filling fractions in this context.
منابع مشابه
On Contact and Symplectic Lie Algeroids
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...
متن کاملOn Integrable c < 1 Open – Closed String Theory
The integrable structure of open–closed string theories in the (p, q) conformal minimal model backgrounds is presented. The relation between the τ–function of the closed string theory and that of the open–closed string theory is uncovered. The resulting description of the open–closed string theory is shown to fit very naturally into the framework of the sl(q,C) KdV hierarchies. In particular, t...
متن کاملGeometric construction of elliptic integrable systems and N = 1∗ superpotentials
We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for AN−1 by Gorsky and Nekrasov to other algebras. This clarifies the role of (twisted) affine Kac-Moody algebras in elliptic Calogero-Moser systems and allows for a natural geometric construction of Lax operators for these systems. We elaborate on the connecti...
متن کاملOrthogonal and Symplectic Matrix Integrals and Coupled KP Hierarchy
Over the past decade, the intimate relationships between matrix integrals and nonlinear integrable systems have been clarified, particularly in the context of string theory. In such cases, nonperturbative properties of physical quantities can be evaluated by the use of the integrable structures of the models. (For review, see refs. 1-4.) Here, we consider a matrix integral over an ensemble of H...
متن کاملMatrix Quantum Mechanics and Two-dimensional String Theory in Non-trivial Backgrounds
String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string theory which can be defined in low dimensions. A particular interesting case is 2D string theory. On the one hand, it has a very rich structure and, on the o...
متن کامل