BPS Operators and Brane Geometries.
Abstract
In this thesis we explore the finite N spectrum of BPS operators in four-dimensional
supersymmetric conformal field theories (CFT), which have dual AdS gravitational descriptions.
In the first part we analyze the spectrum of chiral operators in the free limit of
quiver gauge theories. We find explicit counting formulas at finite N for arbitrary quivers,
construct an orthogonal basis in the free inner product, and derive the chiral ring structure
constants. In order to deal with arbitrarily complicated quivers, we develop convenient
diagrammatic techniques: the results are expressed by associating Young diagrams and
Littlewood-Richardson coefficients to modifications of the original quiver. We develop the
notion of a "quiver character", which is a generalization of the symmetric group character,
obeying analogous orthogonality properties.
In the second part we analyze how the BPS spectrum changes at weak coupling, focusing
on the N = 4 supersymmetric Yang-Mills. We find a formal expression for the
complete set of eighth-BPS operators at finite N, and use it to derive corrections to a
near-BPS operator.
In the third part of this thesis we move on to the strong coupling regime, where
the dual gravitational description applies. The BPS spectrum on the gravity side includes
D3-branes wrapping arbitrary holomorphic surfaces, a generalization of the spherical giant
gravitons. Quantizing this moduli space gives a Hilbert space, which, via duality and nonrenormalization
theorems, should map to the space of BPS operators derived in the weak
coupling regime. We apply techniques from fuzzy geometry to study this correspondence
between D3-brane geometries, quantum states, and BPS operators in field theory
Authors
Pasukonis, JurgisCollections
- Theses [4490]