Hidden symmetries of theAdS5×S5superstring

Abstract

Attempts to solve Yang-Mills theory must eventually face the problem of analyzing the theory at intermediate values of the coupling constant. In this regime neither perturbation theory nor the gravity dual are adequate, and one must consider the full string theory in the appropriate background. We suggest that in some nontrivial cases the world sheet theory may be exactly solvable. For the Green-Schwarz superstring on AdS 5 × S 5 we find an infinite set of nonlocal classically conserved charges, of the type that exist in integrable field theories.

An(1)affine Toda field theories with integrable boundary conditions revisited

“…Generalization of our results for any A (1) n (n > 1) ATFT will be also presented in a separate publication. Finally, a similar exhaustive analysis regarding principal chiral models (partial results maybe found in [46]) will be particularly relevant especially bearing in mind the physical significance of a specific super-symmetric principal chiral model within the AdS/CFT correspondence [47,48]. Also define the fundamental weights µ k = (µ 1 k , .…”

Free fermion resolution of supergroup WZNW models

“…The same class of supergroup σ-models is also known to admit a new kind of marginal deformations that are not of current-current type [23,24]. Finally, there seems to be a striking correspondence between the integrability of these models and their conformal invariance [25,26,21,22].…”

“…Such phenomena appear to be very rare, though. 25 Since the Cartan subalgebra of g was assumed to be identical to the Cartan subalgebra of g0 this statement even holds for unspecialized characters and partition functions.…”

“…Hence, the partition function of the interacting theory agrees with the partition function of the decoupled model and both may be written as a sum over bilinears of characters of Kac modules. 25 Thereby, the partition function of WZNW models on type I supergroups takes the form…”

An exceptional algebraic origin of the AdS/CFT Yangian symmetry

“…On the super Yang-Mills theory side, whose description is valid in the weak 't Hooft coupling region λ = g 2 YM N ≪ 1, the perturbative dilatation operator was mapped to the Hamiltonian of an integrable spin chain model [1] where infinite conserved charges lead to solvability. On the string sigma model side, valid in the strong coupling region λ ≫ 1, flat connection which implies infinite symmetries was also constructed [2]. It was then expected that we can interpolate these two regions by integrability and solve the theory completely.…”