First-principles derivation of the AdS/CFT Y-systems

Abstract

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.Comment: 45 pages, 5 figures; v2: minor additions, JHEP versio

Solving the AdS/CFT Y-system

“…as eigenvalues of Qoperators [37][38][39]. Even though the construction of Q-and T-operators in AdS/CFT is still in a preliminary stage (see [30] for the first nontrivial quantum computation with T-operators), we believe that Q H will play the same role, i.e. it will be an identity operator.…”

“…In the strong coupling limit the T-functions were identified with the psup2, 2|4q characters of the monodromy matrix [17]. This classical monodromy matrix was perturbatively quantized, up to two loops on the world sheet, in [29,30] and the Hirota functional equation (1.1) was shown to hold at least in this approximation.…”

“…Let us remind that there is some evidence [17,30] for interpretation of the T-functions as transfer matrices. In particular, at strong coupling the T-functions are reduced to the characters of classical monodromy matrix, in such a way that each pair of indices pa, sq corresponds to a unitary representation of the symmetry group PSUp2, 2|4q having a rectangular aˆs Young tableau.…”

“…30 One can define ρ2puq " limǫÑ`0Tǫ,1puq. For u P q Z0 the limit is zero since it is equal toT0,1 which must vanish due to Z4.…”

Master symmetry in the AdS 5 × S 5 pure spinor string

“…[14]) than for the pure spinor version. Some interesting results concerning the classical and quantum integrability in the pure spinor formalism are given in references [15][16][17][18]. A possible application of integrability techniques to the quantum pure spinor string is to study its worldsheet dilatation operator [19].…”