Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTwo-dimensional abelian BF theory in Lorenz gauge as a twisted N=(2,2) superconformal field theory
125
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study the two-dimensional topological abelian BF theory in the Lorenz gauge and, surprisingly, we find that the gauged-fixed theory is a free type B twisted N=(2,2) superconformal theory with odd linear target space, with the ghost field c being the pullback of the linear holomorphic coordinate on the target. The BRST operator of the gauge-fixed theory equals the total Q of type B twisted theory. This unexpected identification of two different theories opens a way for nontrivial deformations of both of these theories.
rate research
Read More
We study two-dimensional non-abelian BF theory in Lorenz gauge and prove that it is a topological conformal field theory. This opens the possibility to compute topological string amplitudes (Gromov-Witten invariants). We found that the theory is exactly solvable in the sense that all correlators are given by finite-dimensional convergent integrals. Surprisingly, this theory turns out to be logarithmic in the sense that there are correlators given by polylogarithms and powers of logarithms. Furthermore, we found fields with logarithmic conformal dimension (elements of a Jordan cell for $L_0$). We also found certain vertex operators with anomalous dimensions that depend on the non-abelian coupling constant. The shift of dimension of composite fields may be understood as arising from the dependence of subtracted singular terms on local coordinates. This generalizes the well-known explanation of anomalous dimensions of vertex operators in the free scalar field theory.
The analysis of the large-$N$ limit of $U(N)$ Yang-Mills theory on a surface proceeds in two stages: the analysis of the Wilson loop functional for a simple closed curve and the reduction of more general loops to a simple closed curve. In the case of the 2-sphere, the first stage has been treated rigorously in recent work of Dahlqvist and Norris, which shows that the large-$N$ limit of the Wilson loop functional for a simple closed curve in $S^{2}$ exists and that the associated variance goes to zero. We give a rigorous treatment of the second stage of analysis in the case of the 2-sphere. Dahlqvist and Norris independently performed such an analysis, using a similar but not identical method. Specifically, we establish the existence of the limit and the vanishing of the variance for arbitrary loops with (a finite number of) simple crossings. The proof is based on the Makeenko-Migdal equation for the Yang-Mills measure on surfaces, as established rigorously by Driver, Gabriel, Hall, and Kemp, together with an explicit procedure for reducing a general loop in $S^{2}$ to a simple closed curve. The methods used here also give a new proof of these results in the plane case, as a variant of the methods used by L{e}vy. We also consider loops on an arbitrary surface $Sigma$. We put forth two natural conjectures about the behavior of Wilson loop functionals for topologically trivial simple closed curves in $Sigma.$ Under the weaker of the conjectures, we establish the existence of the limit and the vanishing of the variance for topologically trivial loops with simple crossings that satisfy a smallness assumption. Under the stronger of the conjectures, we establish the same result without the smallness assumption.
We compute some arithmetic path integrals for BF-theory over the ring of integers of a totally imaginary field, which evaluate to natural arithmetic invariants associated to $mathbb{G}_m$ and abelian varieties.
We consider the $mathcal{N}=2$ SYM theory with gauge group SU($N$) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-$N$ t Hooft expansion and is dual to a particular orientifold of $AdS_{5}times S^{5}$. We analyze this gauge theory relying on the matrix model provided by localization a la Pestun. Even though this matrix model has very non-trivial interactions, by exploiting the full Lie algebra approach to the matrix integration, we show that a large class of observables can be expressed in a closed form in terms of an infinite matrix depending on the t Hooft coupling $lambda$. These exact expressions can be used to generate the perturbative expansions at high orders in a very efficient way, and also to study analytically the leading behavior at strong coupling. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to the Pade resummations derived from very long perturbative series, that turn out to be extremely stable beyond the convergence disk $|lambda|<pi^2$ of the latter.
Coincident D3-branes placed at a conical singularity are related to string theory on $AdS_5times X_5$, for a suitable five-dimensional Einstein manifold $X_5$. For the example of the conifold, which leads to $X_5=T^{1,1}=(SU(2)times SU(2))/U(1)$, the infrared limit of the theory on $N$ D3-branes was constructed recently. This is ${cal N}=1$ supersymmetric $SU(N)times SU(N)$ gauge theory coupled to four bifundamental chiral superfields and supplemented by a quartic superpotential which becomes marginal in the infrared. In this paper we consider D3-branes wrapped over the 3-cycles of $T^{1,1}$ and identify them with baryon-like chiral operators built out of products of $N$ chiral superfields. The supergravity calculation of the dimensions of such operators agrees with field theory. We also study the D5-brane wrapped over a 2-cycle of $T^{1,1}$, which acts as a domain wall in $AdS_5$. We argue that upon crossing it the gauge group changes to $SU(N)times SU(N+1)$. This suggests a construction of supergravity duals of ${cal N}=1$ supersymmetric $SU(N_1)times SU(N_2)$ gauge theories.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
