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Register a new userTowards Deconstruction of the Type D (2,0) Theory
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We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional $(2,0)$ theory of type $D_k$. This 4d theory is defined by a necklace quiver with alternating gauge nodes $mathrm{O}(2k)$ and $mathrm{Sp}(k)$. We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of $mathrm{O}$ versus $mathrm{SO}$ gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.
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The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the $A$-type (2,0) theories on $T^2$, starting from a four-dimensional $mathcal N=2$ circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: In the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D $mathcal N=2$ quiver to the half-BPS limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on $S^4$ to the (2,0) partition function on $S^4 times T^2$. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.
We discuss how D=5 maximally supersymmetric Yang-Mills theory (MSYM) might be used to study or even to define the (2,0) theory in six dimensions. It is known that the compactification of (2,0) theory on a circle leads to D=5 MSYM. A variety of arguments suggest that the relation can be reversed, and that all of the degrees of freedom of (2,0) theory are already present in D=5 MSYM. If so, this relation should have consequences for D=5 SYM perturbation theory. We explore whether it might imply all orders finiteness, or else an unusual relation between the cutoff and the gauge coupling. S-duality of the reduction to D=4 may provide nonperturbative constraints or tests of these options.
We study type-B conformal anomalies associated with $frac{1}{2}$-BPS Coulomb-branch operators in 4D $mathcal N=2$ superconformal field theories. When the vacuum preserves the conformal symmetry these anomalies coincide with the two-point function coefficients in the Coulomb-branch chiral ring. They are non-trivial functions of exactly-marginal couplings that can be determined from the $S^4$ partition function. In this paper, we examine the fate of these anomalies in vacua of the Higgs-branch moduli space, where conformal symmetry is spontaneously broken. We argue non-perturbatively that these anomalies are covariantly constant on conformal manifolds. In some cases, this can be used to show that they match in the broken and unbroken phases. Thus, we uncover a new class of data on the Higgs branch of 4D $mathcal N=2$ conformal field theories that are exactly computable. An interesting application of this matching occurs in $mathcal N=2$ circular quivers that deconstruct the 6D (2,0) theory on a torus. In that context, we argue that 4D supersymmetric localisation can be used to calculate non-trivial data involving $frac{1}{2}$-BPS operators of the 6D theory as exact functions of the complex structure of the torus.
We consider a twisted version of the abelian $(2,0)$ theory placed upon a Lorenzian six-manifold with a product structure, $M_6=C times M_4 $. This is done by an investigation of the free tensor multiplet on the level of equations of motion, where the problem of its formulation in Euclidean signature is circumvented by letting the time-like direction lie in the two-manifold $C$ and performing a topological twist along $M_4$ alone. A compactification on $C$ is shown to be necessary to enable the possibility of finding a topological field theory. The hypothetical twist along a Euclidean $C$ is argued to amount to the correct choice of linear combination of the two supercharges scalar on $M_4$. This procedure is expected and conjectured to result in a topological field theory, but we arrive at the surprising conclusion that this twisted theory contains no $Q$-exact and covariantly conserved stress tensor unless $M_4$ has vanishing curvature. This is to our knowledge a phenomenon which has not been observed before in topological field theories. In the literature, the setup of the twisting used here has been suggested as the origin of the conjectured AGT-correspondence, and our hope is that this work may somehow contribute to the understanding of it.
We consider (2,0) theory on a manifold M_6 that is a fibration of a spatial S^1 over some five-dimensional base manifold M_5. Initially, we study the free (2,0) tensor multiplet which can be described in terms of classical equations of motion in six dimensions. Given a metric on M_6 the low energy effective theory obtained through dimensional reduction on the circle is a Maxwell theory on M_5. The parameters describing the local geometry of the fibration are interpreted respectively as the metric on M_5, a non-dynamical U(1) gauge field and the coupling strength of the resulting low energy Maxwell theory. We derive the general form of the action of the Maxwell theory by integrating the reduced equations of motion, and consider the symmetries of this theory originating from the superconformal symmetry in six dimensions. Subsequently, we consider a non-abelian generalization of the Maxwell theory on M_5. Completing the theory with Yukawa and phi^4 terms, and suitably modifying the supersymmetry transformations, we obtain a supersymmetric Yang-Mills theory which includes terms related to the geometry of the fibration.
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