Thermodynamics of the quantum su(1,1)su(1,1) Landau-Lifshitz model

We present thermodynamics of the quantum su(1,1) Landau-Lifshitz model, following our earlier exposition [J. Math. Phys. 50, 103518 (2009)] of the quantum integrability of the theory, which is based on construction of self-adjoint extensions, leading to a regularized quantum Hamiltonian for an arbitrary n-particle sector. Starting from general discontinuity properties of the functions used to construct the self-adjoint extensions, we derive the thermodynamic Bethe Ansatz equations. We show that due to non-symmetric and singular kernel, the self-consistency implies that only negative chemical potential values are allowed, which leads to the conclusion that, unlike its su(2) counterpart, the su(1,1) LL theory at T=0 has no instabilities.Comment: 10 page

Expansion in Feynman Graphs as Simplicial String Theory

We show that the series expansion of quantum field theory in the Feynman diagrams can be explicitly mapped on the partition function of the simplicial string theory -- the theory describing embeddings of the two--dimensional simplicial complexes into the space--time of the field theory. The summation over two--dimensional geometries in this theory is obtained from the summation over the Feynman diagrams and the integration over the Schwinger parameters of the propagators. We discuss the meaning of the obtained relation and derive the one--dimensional analog of the simplicial theory on the example of the free relativistic particle.Comment: Latex, 11pp, Minor mintakes are correcte

Conformal boundary and geodesics for AdS5×S5AdS_5\times S^5 and the plane wave: Their approach in the Penrose limit

Projecting on a suitable subset of coordinates, a picture is constructed in which the conformal boundary of $AdS_5\times S^5$ and that of the plane wave resulting in the Penrose limit are located at the same line. In a second line of arguments all $AdS_5\times S^5$ and plane wave geodesics are constructed in their integrated form. Performing the Penrose limit, the approach of null geodesics reaching the conformal boundary of $AdS_5\times S^5$ to that of the plane wave is studied in detail. At each point these null geodesics of $AdS_5\times S^5$ form a cone which degenerates in the limit.Comment: some statements refined, chapter 5 rewritten to make it more precise, some typos correcte

Holographic three-point functions of giant gravitons

Working within the AdS/CFT correspondence we calculate the three-point function of two giant gravitons and one pointlike graviton using methods of semiclassical string theory and considering both the case where the giant gravitons wrap an S^3 in S^5 and the case where the giant gravitons wrap an S^3 in AdS_5. We likewise calculate the correlation function in N=4 SYM using two Schur polynomials and a single trace chiral primary. We find that the gauge and string theory results have structural similarities but do not match perfectly, and interpret this in terms of the Schur polynomials' inability to interpolate between dual giant and pointlike gravitons.Comment: 21 page

BMN operators and string field theory

We extract from gauge theoretical calculations the matrix elements of the SYM dilatation operator. By the BMN correspondence this should coincide with the 3-string vertex of light cone string field theory in the pp-wave background. We find a mild but important discrepancy with the SFT results. If the modified $O(g_2)$ matrix elements are used, the $O(g_2^2)$ anomalous dimensions are exactly reproduced without the need for a contact interaction in the single string sector.Comment: 11 pages; v2: references adde

Quasilocality of joining/splitting strings from coherent states

Using the coherent state formalism we calculate matrix elements of the one-loop non-planar dilatation operator of ${\cal N}=4$ SYM between operators dual to folded Frolov-Tseytlin strings and observe a curious scaling behavior. We comment on the {\it qualitative} similarity of our matrix elements to the interaction vertex of a string field theory. In addition, we present a solvable toy model for string splitting and joining. The scaling behaviour of the matrix elements suggests that the contribution to the genus one energy shift coming from semi-classical string splitting and joining is small.Comment: 17 pages, 7 figures in 11 file

Beyond the Planar Limit in ABJM

In this article we consider gauge theories with a U(N)X U(N) gauge group. We provide, for the first time, a complete set of operators built from scalar fields that are in the bi fundamental of the two groups. Our operators diagonalize the two point function of the free field theory at all orders in 1/N. We then use this basis to investigate non-planar anomalous dimensions in the ABJM theory. We show that the dilatation operator reduces to a set of decoupled harmonic oscillators, signaling integrability in a nonplanar large N limit.Comment: v2: minor revisison

Predictions for PP-wave string amplitudes from perturbative SYM

The role of general two-impurity multi-trace operators in the BMN correspondence is explored. Surprisingly, the anomalous dimensions of all two-impurity multi-trace BMN operators to order g_2^2\lambda' are completely determined in terms of single-trace anomalous dimensions. This is due to suppression of connected field theory diagrams in the BMN limit and this fact has important implications for some string theory processes on the PP-wave background. We also make gauge theory predictions for the matrix elements of the light-cone string field theory Hamiltonian in the two string-two string and one string-three string sectors.Comment: 46 pages, 12 figures. V3:typos correcte