7 research outputs found
Entanglement Structure of Deconfined Quantum Critical Points
We study the entanglement properties of deconfined quantum critical points.
We show not only that these critical points may be distinguished by their
entanglement structure but also that they are in general more highly entangled
that conventional critical points. We primarily focus on computations of the
entanglement entropy of deconfined critical points in 2+1 dimensions, drawing
connections to topological entanglement entropy and a recent conjecture on the
monotonicity under RG flow of universal terms in the entanglement entropy. We
also consider in some detail a variety of issues surrounding the extraction of
universal terms in the entanglement entropy. Finally, we compare some of our
results to recent numerical simulations.Comment: 12 pages, 4 figure
Yang--Baxter symmetry in integrable models: new light from the Bethe Ansatz solution
We show how any integrable 2D QFT enjoys the existence of infinitely many
non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry
algebra. These charges are generated by quantum monodromy operators and provide
a representation of deformed affine Lie algebras. We review and generalize
the work of de Vega, Eichenherr and Maillet on the bootstrap construction of
the quantum monodromy operators to the sine--Gordon (or massive Thirring)
model, where such operators do not possess a classical analogue. Within the
light--cone approach to the mT model, we explicitly compute the eigenvalues of
the six--vertex alternating transfer matrix \tau(\l) on a generic physical
state, through algebraic Bethe ansatz. In the thermodynamic limit \tau(\l)
turns out to be a two--valued periodic function. One determination generates
the local abelian charges, including energy and momentum, while the other
yields the abelian subalgebra of the (non--local) YB algebra. In particular,
the bootstrap results coincide with the ratio between the two determinations of
the lattice transfer matrix.Comment: 30 page
Zonotopes and four-dimensional superconformal field theories
The a-maximization technique proposed by Intriligator and Wecht allows us to
determine the exact R-charges and scaling dimensions of the chiral operators of
four-dimensional superconformal field theories. The problem of existence and
uniqueness of the solution, however, has not been addressed in general setting.
In this paper, it is shown that the a-function has always a unique critical
point which is also a global maximum for a large class of quiver gauge theories
specified by toric diagrams. Our proof is based on the observation that the
a-function is given by the volume of a three dimensional polytope called
"zonotope", and the uniqueness essentially follows from Brunn-Minkowski
inequality for the volume of convex bodies. We also show a universal upper
bound for the exact R-charges, and the monotonicity of a-function in the sense
that a-function decreases whenever the toric diagram shrinks. The relationship
between a-maximization and volume-minimization is also discussed.Comment: 29 pages, 15 figures, reference added, typos corrected, version
published in JHE
The nonperturbative functional renormalization group and its applications
The renormalization group plays an essential role in many areas of physics,
both conceptually and as a practical tool to determine the long-distance
low-energy properties of many systems on the one hand and on the other hand
search for viable ultraviolet completions in fundamental physics. It provides
us with a natural framework to study theoretical models where degrees of
freedom are correlated over long distances and that may exhibit very distinct
behavior on different energy scales. The nonperturbative functional
renormalization-group (FRG) approach is a modern implementation of Wilson's RG,
which allows one to set up nonperturbative approximation schemes that go beyond
the standard perturbative RG approaches. The FRG is based on an exact
functional flow equation of a coarse-grained effective action (or Gibbs free
energy in the language of statistical mechanics). We review the main
approximation schemes that are commonly used to solve this flow equation and
discuss applications in equilibrium and out-of-equilibrium statistical physics,
quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure