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Register a new userTwo dimensional RG flows and Yang-Mills instantons
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We study RG flow solutions in (1,0) six dimensional supergravity coupled to an anti-symmetric tensor and Yang-Mills multiplets corresponding to a semisimple group $G$. We turn on $G$ instanton gauge fields, with instanton number $N$, in the conformally flat part of the 6D metric. The solution interpolates between two (4,0) supersymmetric $AdS_3times S^3$ backgrounds with two different values of $AdS_3$ and $S^3$ radii and describes an RG flow in the dual 2D SCFT. For the single instanton case and $G=SU(2)$, there exist a consistent reduction ansatz to three dimensions, and the solution in this case can be interpreted as an uplifted 3D solution. Correspondingly, we present the solution in the framework of N=4 $(SU(2)ltimes mathbf{R}^3)^2$ three dimensional gauged supergravity. The flows studied here are of v.e.v. type, driven by a vacuum expectation value of a (not exactly) marginal operator of dimension two in the UV. We give an interpretation of the supergravity solution in terms of the D1/D5 system in type I string theory on K3, whose effective field theory is expected to flow to a (4,0) SCFT in the infrared.
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By constructing the configuration of D3-branes with D(-1)-branes as D-instantons, we study the three-dimensional Yang-Mills Chern-Simons theory in holography. Due to the presence of the D-instantons, the D7-branes with discrepant embedding functions are able to be introduced in order to include the fundamental fermions (as flavors) and the Chern-Simons term (at very low energy) in the dual theory. The vacuum structure at zero temperature is studied in the soliton background and it illustrates the topological phase transition in the presence of instantons. Moreover, since the confinement/deconfinement phase transition could be holographically identified as the Hawking-Page transition in the bulk, we accordingly calculate the critical temperature of the deconfinement phase transition by collecting the bulk onshell action as the thermodynamical free energy. On the other hand, we evaluate the difference of the entanglement entropy in slab configuration by using the RT formula since the confinement may also be characterized by the entanglement entropy. Altogether we find the behavior of the critical temperature is in qualitative agreement with the behavior of the critical length determined by the entanglement entropy which implies the entanglement entropy could indeed be a character of the confinement in our setup and the D3-D(-1) system would be a remarkable approach to study the three-dimensional gauge 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.
It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R^{3,1}. We show that such solutions exist in SU(N) gauge theory on the spaces R^2times S^2 and R^1times S^1times S^2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T^1times S^2, where T^1 is R^1 or S^1. Namely, imposing SO(3)-invariance and some reality conditions, we consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the phi^4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R^{1,1}times S^2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R^1times S^1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S^1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R^1times S^1times S^2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). We also describe similar solutions in Euclidean SU(N) gauge theory on S^1times S^3 interpreted as chains of n instanton-antiinstanton pairs.
We consider two-dimensional Yang-Mills theories on arbitrary Riemann surfaces. We introduce a generalized Yang-Mills action, which coincides with the ordinary one on flat surfaces but differs from it in its coupling to two-dimensional gravity. The quantization of this theory in the unitary gauge can be consistently performed taking into account all the topological sectors arising from the gauge-fixing procedure. The resulting theory is naturally interpreted as a Matrix String Theory, that is as a theory of covering maps from a two-dimensional world-sheet to the target Riemann surface.
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group.
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