Spin Chain Sigma Model Research Articles

Superstring sigma models from spin chains: the [formula omitted] case

We derive the coherent state representation of the integrable spin chain Hamiltonian with non-compact supersymmetry group G = SU ( 1 , 1 | 1 ) . By passing to the continuous limit, we find a spin chain sigma model describing a string moving on the supercoset G / H , H being the stabilizer group. The action is written in a manifestly G-invariant form in terms of the Cartan forms and the string coordinates in the supercoset. The spin chain sigma model is shown to agree with that following from the Green–Schwarz action describing two-charged string spinning on AdS 5 × S 5 .

A NOTE ON SPIN CHAIN/STRING DUALITY

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N = 4 SYM and rotating strings was made. The correspondence was established mainly by use of Bethe ansatz technique applied to the spin s Heisenberg chain model. In a recent paper,16 the author suggested to solve the Heisenberg model by use of sigma model approach. In this current work we generalize the solutions presented in Ref. 16 and comment on the dual string theory. It turns out that our solution is related to a generalized ansatz for rotating strings which can be reduced to the so-called Neumann–Rosochatius integrable system. We comment on the spin chain sigma model and string solutions and the possibilities for a more precise formulation of the string/gauge theory correspondence.

The SU(2|3) spin chain sigma model

AbstractThe one‐loop planar dilatation operator of 𝒩 = 4 supersymmetric Yang‐Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) spin chain. We construct the non‐linear sigma model describing the continuum limit of the SU(2|3) subsector of the 𝒩 = 4 chain. We explicitly identify the spin chain sigma model with the one for a superstring moving in AdS5 × S5 with large angular momentum along the five‐sphere.

Spin chain sigma models with fermions

The complete one-loop planar dilatation operator of N=4 supersymmetric Yang-Mills is isomorphic to the hamiltonian of an integrable PSU(2,2|4) quantum spin chain. We construct the non-linear sigma models describing the continuum limit of the SU(1|3) and SU(2|3) sectors of the complete N=4 chain. We explicitely identify the spin chain sigma model with the one for a superstring moving in AdS_5xS^5 with large angular momentum along the five-sphere.

SL(2) spin chain and spinning strings on [formula omitted

We derive the coherent state representation of the integrable spin chain Hamiltonian with symmetry group SL ( 2 , R ) . By passing to the continuum limit, we find a spin chain sigma model describing a string moving on the hyperboloid SL ( 2 , R ) / U ( 1 ) . The same sigma model is found by considering strings rotating with large angular momentum in AdS 5 × S 5 . The spinning strings are identified with semiclassical coherent states built out of SL ( 2 , R ) spin chain states.

Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models

From the SU(2) spin chain sigma model at the one-loop and two-loop orders we recover the classical circular string solution with two S5 spins (J1,J2) in the AdS5 ? S5 string theory. In the SL(2) sector of the one-loop spin chain sigma model we explicitly construct a solution which corresponds to the folded string solution with one AdS5 spin S and one S5 spin J. In the one-loop general sigma model we demonstrate that there exists a solution which reproduces the energy of the circular constant-radii string solution with three spins (S1,S2,J).

The circular, elliptic three-spin string from the [formula omitted] spin chain

We complete the description of the circular, elliptic three spin string on AdS5×S5 having three large angular momenta (J1,J2,J3) on S5 in the language of the integrable SU(3) spin chain. First, we recover the string solution directly from the spin chain sigma model and secondly, we identify the appropriate Bethe root configuration in the so far unexplored region of parameter space.

The SU(3) spin chain sigma model and string theory

The ferromagnetic integrable SU(3) spin chain provides the one loop anomalous dimension of single trace operators involving the three complex scalars of N=4 supersymmetric Yang-Mills. We construct the non-linear sigma model describing the continuum limit of the SU(3) spin chain. We find that this sigma model corresponds to a string moving with large angular momentum in the five-sphere in AdS_5xS^5. The energy and spectrum of fluctuations for rotating circular strings with angular momenta along three orthogonal directions of the five-sphere is reproduced as a particular case from the spin chain sigma model.