285 research outputs found
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 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
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