UC Berkeley

I will present three studies of string theory on twisted geometries.

In the first calculation included in this dissertation we use gauge/gravity duality

to study the Coulomb branch of an unusual type of nonlocal field theory, called Puff

Field Theory. On the gravity side, this theory is given in terms of D3-branes in

type IIB string theory with a geometric twist. While the field theory description,

available in the IR limit, is a deformation of Yang-Mills gauge theory by an order

seven operator which we here compute.

In the rest of this disertation we explore N = 4 super Yang-Mills (SYM) theory

compactied on a circle with S-duality and R-symmetry twists that preserve N = 6

supersymmetry in 2 + 1D. It was shown that abelian theory on a flat manifold gives

Chern-Simons theory in the low-energy limit and here we are interested in the non-

abelian counterpart. To that end, we introduce external static supersymmetric quark

and anti-quark sources into the theory and calculate the Witten Index of the resulting

Hilbert space of ground states on a two-torus. Using these results we compute the ac-

tion of simple Wilson loops on the Hilbert space of ground states without sources. In

some cases we find disagreement between our results for the Wilson loop eigenvalues

and previous conjectures about a connection with Chern-Simons theory.

The last result discussed in this dissertation demonstrates a connection between

gravitational Chern-Simons theory and N = 4 four-dimensional SYM theory com-

pactified on a circle twisted by S-duality where the remaining three-manifold is not

flat starting with the explicit geometric realization of S-duality in terms of (2, 0)

theory.