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.Comment: 16 pages. Latex. v2: Misprints corrected and references adde

Tensor renormalization group in bosonic field theory

We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.Comment: 5+8 pages, 4+2 figure

Duality of Chiral N=1 Supersymmetric Gauge Theories via Branes

Using a six-orientifold on top of a NS-fivebrane we construct a chiral N=1 supersymmetric gauge theory in four dimensions with gauge group SU(N_c) and matter in the symmetric, antisymmetric and (anti)fundamental representations. Anomaly cancellation is fulfilled by the requirement of a smooth RR 7-form charge distribution and leads us to the introduction of 8 half D-sixbranes ending on the NS-fivebrane. We obtain the dual model from branes by a linking number argument. We check explicitly the 't Hooft anomaly matching conditions and the map between deformations in the original and the dual model.Comment: 16 pages, 2 figures, TeX, harvmac, table

Supersymmetric Gauge Theories from Branes and Orientifold Six-planes

We study brane configurations in the presence of orientifold six-planes. After deriving the curves for N=2 supersymmetric SU(Nc) gauge theories with one flavor in the symmetric or antisymmetric representation and Nf fundamental flavors, we rotate the brane configuration, reducing the supersymmetry to N=1. For the case of an antisymmetric flavor and less than two fundamental flavors, nonperturbative effects lead to a brane configuration that is topologically a torus. Using the description of the orientifold six-planes as Dn singularities we discuss the Higgs branches for N=2 brane configurations with Sp/SO gauge groups and the related N=1 theories with tensor representations.Comment: 30 pages (harvmac b-mode), 5 figures, (v2 minor corrections), (v3 sign error corrected

Instability of Non-Commutative SYM Theories at Finite Temperature

We extend our previous work on the quasi-particle excitations in N=4 non-commutative U(1) Yang-Mills theory at finite temperature. We show that above some critical temperature there is a tachyon in the spectrum of excitations. It is a collective transverse photon mode polarized in the non-commutative plane. Thus the theory seems to undergo a phase transition at high temperature. Furthermore we find that the group velocity of quasi-particles generically exceeds the speed of light at low momentum.Comment: 23 pages (harvmac b-mode), 5 figures, v2: discussion on U(N) theories and matter in fundamental representation added, misprints corrected, references added v3: reference adde

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

N=4 supersymmetric Yang-Mills operators carrying large charges are dual to semiclassical strings in AdS_5xS^5. The spectrum of anomalous dimensions of very large operators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.Comment: 18 pages. Latex. v2: Misprints corrected, expanded discussions with comments on end point effects, and updated referenc

Holographic Relaxation of Finite Size Isolated Quantum Systems

We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the traveling shell is brought into correspondence with the evolution of the entanglement pattern in the dual field theory. The entanglement entropy is not only able to portrait the streaming of entangled excitations, but it is also a useful probe of interaction effects.Comment: 37 pages, 27 figure

Integrability and scattering of the boson field theory on a lattice

A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of exactly solvable models, that are currently applied to spin systems, to a massless and massive free boson on a 2D lattice. The Boltzmann weights of the model are shown to satisfy the Yang-Baxter equation with a uniformization given by trigonometric functions in the massless case, and Jacobi elliptic functions in the massive case. We diagonalize the row-to-row transfer matrix, derive the conserved quantities, and implement the quantum inverse scattering method. Finally, we construct two factorized scattering $S$ matrix models for continuous degrees of freedom using trigonometric and elliptic functions. These results place the free boson model in 2D in the same position as the rest of the models that are exactly solvable \`a la Yang-Baxter, offering possible applications in quantum computation.Comment: 32 pages, 4 figure