Four-dimensional Super Yang-Mills Theory Research Articles

VOAs labelled by complex reflection groups and 4d SCFTs

We define and study a class of mathcal{N} = 2 vertex operator algebras {mathcal{W}}_{mathrm{G}} labelled by complex reflection groups. They are extensions of the mathcal{N} = 2 super Virasoro algebra obtained by introducing additional generators, in correspondence with the invariants of the complex reflection group G. If G is a Coxeter group, the mathcal{N} = 2 super Virasoro algebra enhances to the (small) mathcal{N} = 4 superconformal algebra. With the exception of G = ℤ2, which corresponds to just the mathcal{N} = 4 algebra, these are non-deformable VOAs that exist only for a specific negative value of the central charge. We describe a free-field realization of {mathcal{W}}_{mathrm{G}} in terms of rank(G) βγbc ghost systems, generalizing a construction of Adamovic for the mathcal{N} = 4 algebra at c = −9. If G is a Weyl group, {mathcal{W}}_{mathrm{G}} is believed to coincide with the mathcal{N} = 4 VOA that arises from the four-dimensional super Yang-Mills theory whose gauge algebra has Weyl group G. More generally, if G is a crystallographic complex reflection group, {mathcal{W}}_{mathrm{G}} is conjecturally associated to an mathcal{N} = 3 4d superconformal field theory. The free-field realization allows to determine the elusive “R-filtration” of {mathcal{W}}_{mathrm{G}} , and thus to recover the full Macdonald index of the parent 4d theory.

Loop space, (2,0) theory, and solitonic strings

We present an interacting action that lives in loop space, and we argue that this is a generalization of the theory for a free tensor multiplet. From this action we derive the Bogomolnyi equation corresponding to solitonic strings. Using the Hopf map, we find a correspondence between BPS strings and BPS monopoles in four-dimensional super Yang-Mills theory. This enable us to find explicit BPS saturated solitonic string solutions.

D=4 gauge theory correlators from D=10 NSR σ-model

In our previous work (hep-th/9812044) we have proposed the sigma-model action, conjectured to be the NSR analogue of superstring theory on AdS 5× S 5. This sigma-model is the NSR superstring action with potential term corresponding to the exotic 5-form vertex operator (branelike state). This 5-form potential plays the role of cosmological term, effectively curving the flat space-time geometry to that of AdS 5× S 5. In this paper we study this ansatz in more details and provide the derivation of the correlators of the four-dimensional super Yang-Mills theory from the above mentioned sigma-model. In particular, we show that the correlation function of two dilaton vertex operators in such a model reproduces the well-known result of the two-point function in the N=4 four-dimensional super Yang-Mills theory: 〈F 2(x)F 2(y)〉∼ N 2 |x−y| 8 .

Solving four-dimensional field theories with the Dirichlet fivebrane

The realization of $\mathcal{N}=2$ four-dimensional super Yang-Mills theories in terms of a single Dirichlet fivebrane in type-IIB string theory is considered. A classical brane computation reproduces the full quantum low-energy effective action. This result has a simple explanation in terms of mirror symmetry.

Gauge dependence of the Nicolai map in super Yang-Mills theory

Four-dimensional super Yang-Mills theory is reformulated in terms of the self-dual field strengths by deriving an effective action in an arbitrary gauge. With the exception of the light cone gauges, this action is in general non-gaussian and, typically, non-local.