We conjecture that local theta correspondence can be normalized by the leading coefficient of a weighted local period integral, and that there exists a duality of local and global inner product formulas. The conjecture is verified for the pair ( SL2, PGL2) and (SL2, SO(2, 2)). As an application, global inner product formulas are obtained for liftings in the directions PGL2 → SL2, GSO(2, 2) → GL2.

By a Riemann mapping we mean an analytic function which is defined and univalent on the unit disk. Such a function is said to be normalized if it has value zero and positive derivative at the origin. We are concerned with normalized Riemann mappings of the unit disk into itself. If B(z) is such a function, the operator f(z) into f(B(z)) maps the Dirichlet space contractively into itself. Elemen...

A massive version of T-duality in six dimensions is given, that maps the K3 compactification of Romans’ theory onto the K3 compactification of Type IIB theory. This is done by performing a (standard) Kaluza-Klein reduction on six-dimensional massive Type IIA and a Scherk-Schwarz reduction on Type IIB, mapping both theories onto the same fivedimensional theory. We also comment shortly on the dif...

A tubular D3-brane with electromagnetic flux is considered. It is verified that the quantized electric and magnetic charges are the F-string and D-string charges of the brane, respectively. The D3-brane with parallel electric and magnetic fields collapses to the bound state of strings. A D3-brane with nonzero Poynting vector can be viewed as expanded FD strings. A fundamental string is viewed a...

We study the spectrum of BPS states in N =4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T 3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in this model exhibits a (partially hidden) SL(5,Z) duality symmetry. Besides the electro-magnetic symmetry, this duality group also contains Nahm-like transf...

We analyse supermembrane instantons (fully wrapped supermembranes) by computing the partition function of the three-dimensional supersymmetrical U(N) matrix model under periodic boundary conditions. By mapping the model to a cohomological field theory and considering a mass-deformation of the model, we show that the partition function exactly leads to the U-duality invariant measure factor ente...

We give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions (polyFock spaces), displaying a ”Nyquist rate” which increases with the degree of polyanaliticity. This is done introducing a unitary mapping between vector valued Hilbert spaces and poly-Fock spaces. This mapping extends Bargmann ́s theory to polyanalytic spaces. T...

We study boson–fermion dualities in one-dimensional many-body problems of identical particles interacting only through two-body contacts. By using the path-integral formalism as well configuration-space approach to indistinguishable particles, we find a generalization duality between Lieb–Liniger model and Cheon–Shigehara model. present an explicit construction n-boson n-fermion models which ar...

Title of dissertation: DUALITY METHODS IN NETWORKS, COMPUTER SCIENCE MODELS, AND DISORDERED CONDENSED MATTER SYSTEMS Joe Mitchell, Doctor of Philosophy, 2014 Dissertation directed by: Dr. V. M. Galitski Department of Physics In this thesis, I explore lattice independent duality and systems to which it can be applied. I first demonstrate classical duality on models in an external field, includin...