Supersymmetric probes of wrapped M5-brane backgrounds

Abstract

In this thesis we consider supersymmetric probes in backgrounds sourced by an M5-brane which is wrapped on holomorphic 2-cycles in C(^2) and C(^3), respectively. For the first case, we use M2-brane probes to compute the BPS spectra of the corresponding N = 2 gauge theory, as well as M5-brane probes to calculate field theory parameters such as the gauge coupling, theta angle and complex scalar moduli space metric. This background describes a large class of Hanany-Witten models when dimensionally reduced to Type IIA ten-dimensional supergravity. We calculate the instanton action using a Euclidean DO-brane probe in this limit. For the case of an M5-brane wrapping a 2-cycle in C(^3), we firstly show an alternative method of deriving this solution which involves the projection conditions and certain spinor bilinear differential equations. We also consider M5-brane probes in this background, and analyse the corresponding N = I MQCD gauge theory parameters, in direct analogy with the N = 2 case. We then move on to consider the central charges of the supersymmetry algebra of brane probes in the two backgrounds under consideration. For the case of an M5-brane wrapping a 2-cycle in c2, we find it allows for M2- braneร representing BPS monopoles and vortices. There is also the possibility of a "hidden" M5-brane which is similar to the M2-brane, but which includes a rotation in the complex structure and an extra volume modulus. For the N = I case, we find it allows for a supersymmetric M5-brane probe wrapping a Cayley calibrated 4-cycle, which is interpreted as a system of intersecting domain walls. These results are geometrically linked to M-theory structure groups.