A Duality Web in Condensed Matter Systems

We study various dualities in condensed matter systems. The dualities in three dimensions could be derived from a conjecture of a duality between a Dirac fermion theory and an interacting scalar field theory at the Wilson-Fisher fixed point and zero temperature in three dimensions. We show that the dualities are not affected by the non-trivial holonomy, use a mean-field method to study, and discuss the dualities at a finite temperature. Finally, we combine a bulk theory, which is an Abelian $p$-form theory with a theta term in $2p+2$ dimensions, and a boundary theory, which is a $2p+1$ dimensional theory, to discuss constraints and difficulties of a duality web in $2p+1$ dimensions.Comment: 32 page

S-Duality for D3-Brane in NS-NS and R-R Backgrounds

We construct the low-energy effective field theory for a D3-brane in constant R-R 2-form potential background as the S-dual theory of a D3-brane in NS-NS B-field background. Despite the non-Abelian algebra of the noncommutative U(1) gauge symmetry, the electromagnetic duality transformation can be carried out to all orders, and the dual Lagrangian is given in a compact form. The gauge algebra is found to be a mixture of a deformed area-preserving diffeomorphism and the usual U(1) gauge symmetry.Comment: 29 pages, minor change

Geometric Low-Energy Effective Action in a Doubled Spacetime

The ten-dimensional supergravity theory is a geometric low-energy effective theory and the equations of motion for its fields can be obtained from string theory by computing $\beta$ functions. With $d$ compact dimensions, we can add to it an $O(d, d;\mathbb{Z})$ geometric structure and construct the supergravity theory inspired by double field theory through the use of a suitable commutative star product. The latter implements the weak constraint of the double field theory on its fields and gauge parameters in order to have a closed gauge symmetry algebra. The consistency of the action here proposed is based on the orthogonality of the momenta associated with fields in their triple star products in the cubic terms defined for $d\ge1$. This orthogonality holds also for an arbitrary number of star products of fields for $d=1$. Finally, we extend our analysis to the double sigma model, non-commutative geometry and open string theory.Comment: 27 pages, minor changes, references adde