178 research outputs found
Definition of Chern-Simons Terms in Thermal QED_3 Revisited
We present two compact derivations of the correct definition of the
Chern-Simons term in the topologically non trivial context of thermal .
One is based on a transgression descent from a D=4 background connection, the
other on embedding the abelian model in SU(2). The results agree with earlier
cohomology conclusions and can be also used to justify a recent simple
heuristic approach. The correction to the naive Chern-Simons term, and its
behavior under large gauge transformations are displayed.Comment: 9 pages, RevTex, no figures, new derivation from non abelian
embedding adde
A matrix model for the latitude Wilson loop in ABJM theory
In ABJ(M) theory, we propose a matrix model for the exact evaluation of BPS
Wilson loops on a latitude circular contour, so providing a new weak-strong
interpolation tool. Intriguingly, the matrix model turns out to be a particular
case of that computing torus knot invariants in Chern-Simons
theory. At weak coupling we check our proposal against a three-loop
computation, performed for generic framing, winding number and representation.
The matrix model is amenable of a Fermi gas formulation, which we use to
systematically compute the strong coupling and genus expansions. For the
fermionic Wilson loop the leading planar behavior agrees with a previous string
theory prediction. For the bosonic operator our result provides a clue for
finding the corresponding string dual configuration. Our matrix model is
consistent with recent proposals for computing Bremsstrahlung functions exactly
in terms of latitude Wilson loops. As a by-product, we extend the conjecture
for the exact Bremsstrahlung function to generic
representations and test it with a four-loop perturbative computation. Finally,
we propose an exact prediction for at unequal gauge group ranks.Comment: 73 pages; v2: several improvements, JHEP published versio
Correlators of Hopf Wilson loops in the AdS/CFT correspondence
We study at quantum level correlators of supersymmetric Wilson loops with
contours lying on Hopf fibers of . In SYM theory the
strong coupling analysis can be performed using the AdS/CFT correspondence and
a connected classical string surface, linking two different fibers, is
presented. More precisely, the string solution describes oppositely oriented
fibers with the same scalar coupling and depends on an angular parameter,
interpolating between a non-BPS configuration and a BPS one. The system can be
thought as an alternative deformation of the ordinary antiparallel lines giving
the static quark-antiquark potential, that is indeed correctly reproduced, at
weak and strong coupling, as the fibers approach one another.Comment: 38 pages, 5 figure
BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
We study a family of circular BPS Wilson loops in N=6 super
Chern-Simons-matter theories, generalizing the usual 1/2-BPS circle. The scalar
and fermionic couplings depend on two deformation parameters and these
operators can be considered as the ABJ(M) counterpart of the DGRT latitudes
defined in N=4 SYM. We perform a complete two-loop analysis of their vacuum
expectation value, discuss the framing dependence and propose a general
relation with cohomologically equivalent bosonic operators. We make an all-loop
proposal for computing the Bremsstrahlung function associated to the 1/2-BPS
cusp in terms of these generalized Wilson loops. When applied to our two-loop
result it reproduces the known expression. Finally, we comment on the
generalization of this proposal to the bosonic 1/6-BPS case.Comment: 46 pages, 6 figures; references adde
The quantum 1/2 BPS Wilson loop in Chern-Simons-matter theories
In three dimensional Chern-Simons-matter theories two
independent fermionic Wilson loop operators can be defined, which preserve half
of the supersymmetry charges and are cohomologically equivalent at classical
level. We compute their three-loop expectation value in a convenient color
sector and prove that the degeneracy is uplifted by quantum corrections. We
expand the matrix model prediction in the same regime and by comparison we
conclude that the quantum 1/2 BPS Wilson loop is the average of the two
operators. We provide an all-loop argument to support this claim at any order.
As a by-product, we identify the localization result at three loops as a
correction to the framing factor induced by matter interactions. Finally, we
comment on the quantum properties of the non-1/2 BPS Wilson loop operator
defined as the difference of the two fermionic ones.Comment: 22 pages + appendixes, 4 figures, 1 Tabl
Morita Duality and Noncommutative Wilson Loops in Two Dimensions
We describe a combinatorial approach to the analysis of the shape and
orientation dependence of Wilson loop observables on two-dimensional
noncommutative tori. Morita equivalence is used to map the computation of loop
correlators onto the combinatorics of non-planar graphs. Several
nonperturbative examples of symmetry breaking under area-preserving
diffeomorphisms are thereby presented. Analytic expressions for correlators of
Wilson loops with infinite winding number are also derived and shown to agree
with results from ordinary Yang-Mills theory.Comment: 32 pages, 9 figures; v2: clarifying comments added; Final version to
be published in JHE
Towards the exact Bremsstrahlung function of ABJM theory
We present the three-loop calculation of the Bremsstrahlung function
associated to the 1/2-BPS cusp in ABJM theory, including color subleading
corrections. Using the BPS condition we reduce the computation to that of a
cusp with vanishing angle. We work within the framework of heavy quark
effective theory (HQET) that further simplifies the analytic evaluation of the
relevant cusp anomalous dimension in the near-BPS limit. The result passes
nontrivial tests, such as exponentiation, and is in agreement with the
conjecture made in [1] for the exact expression of the Bremsstrahlung function,
based on the relation with fermionic latitude Wilson loops.Comment: 46 pages, 15 figure
The Renormalization of Non-Commutative Field Theories in the Limit of Large Non-Commutativity
We show that renormalized non-commutative scalar field theories do not reduce
to their planar sector in the limit of large non-commutativity. This follows
from the fact that the RG equation of the Wilson-Polchinski type which
describes the genus zero sector of non-commutative field theories couples
generic planar amplitudes with non-planar amplitudes at exceptional values of
the external momenta. We prove that the renormalization problem can be
consistently restricted to this set of amplitudes. In the resulting
renormalized theory non-planar divergences are treated as UV divergences
requiring appropriate non-local counterterms. In 4 dimensions the model turns
out to have one more relevant (non-planar) coupling than its commutative
counterpart. This non-planar coupling is ``evanescent'': although in the
massive (but not in the massless) case its contribution to planar amplitudes
vanishes when the floating cut-off equals the renormalization scale, this
coupling is needed to make the Wilsonian effective action UV finite at all
values of the floating cut-off.Comment: 35 pages, 8 figures; typos correcte
Hard Non-commutative Loops Resummation
The non-commutative version of the euclidean theory is
considered. By using Wilsonian flow equations the ultraviolet renormalizability
can be proved to all orders in perturbation theory. On the other hand, the
infrared sector cannot be treated perturbatively and requires a resummation of
the leading divergencies in the two-point function. This is analogous to what
is done in the Hard Thermal Loops resummation of finite temperature field
theory. Next-to-leading order corrections to the self-energy are computed,
resulting in contributions in the massless case, and
in the massive one.Comment: 4 pages, 3 figures. The resummation procedure is now discussed also
at finite ultraviolet cut-off. Minor changes in abstract and references.
Final version to be published in Physical Review Letter
Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
The twisted Eguchi-Kawai (TEK) model provides a non-perturbative definition
of noncommutative Yang-Mills theory: the continuum limit is approached at large
by performing suitable double scaling limits, in which non-planar
contributions are no longer suppressed. We consider here the two-dimensional
case, trying to recover within this framework the exact results recently
obtained by means of Morita equivalence. We present a rather explicit
construction of classical gauge theories on noncommutative toroidal lattice for
general topological charges. After discussing the limiting procedures to
recover the theory on the noncommutative torus and on the noncommutative plane,
we focus our attention on the classical solutions of the related TEK models. We
solve the equations of motion and we find the configurations having finite
action in the relevant double scaling limits. They can be explicitly described
in terms of twist-eaters and they exactly correspond to the instanton solutions
that are seen to dominate the partition function on the noncommutative torus.
Fluxons on the noncommutative plane are recovered as well. We also discuss how
the highly non-trivial structure of the exact partition function can emerge
from a direct matrix model computation. The quantum consistency of the TEK
formulation is eventually checked by computing Wilson loops in a particular
limit.Comment: 41 pages, JHEP3. Minor corrections, references adde
- …