BPS states in Matrix Strings

Matrix string theory (or more generally U-Duality) requires Super Yang-Mills theory to reflect a stringy degeneracy of BPS short multiplets. These are found as supersymmetric states in the Yang-Mills carrying (fractionated) momentum, or in some cases, instanton number. Their energies also agree with those expected from M(atrix) theory. A nice parallel also emerges in the relevant cases, between momentum and instanton number, (both integral as well as fractional) providing evidence for a recent conjecture relating the two.Comment: Harvmac, 14 pages (big

Guessing under source uncertainty

This paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided. The only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family. A notion of redundancy is first defined and a new divergence quantity that measures this redundancy is identified. This divergence quantity shares the Pythagorean property with the Kullback-Leibler divergence. Good guessing strategies that minimize the supremum redundancy (over the family) are then identified. The min-sup value measures the richness of the uncertainty set. The min-sup redundancies for two examples - the families of discrete memoryless sources and finite-state arbitrarily varying sources - are then determined.Comment: 27 pages, submitted to IEEE Transactions on Information Theory, March 2006, revised September 2006, contains minor modifications and restructuring based on reviewers' comment

N=1{\cal N}=1 Theories and a Geometric Master Field

We study the large $N$ limit of the class of U(N) {\CN}=1 SUSY gauge theories with an adjoint scalar and a superpotential $W(\P)$. In each of the vacua of the quantum theory, the expectation values \laTr$\Phi^p$\ra are determined by a master matrix $\Phi_0$ with eigenvalue distribution \rho_{GT}(\l). \rho_{GT}(\l) is quite distinct from the eigenvalue distribution \rho_{MM}(\l) of the corresponding large $N$ matrix model proposed by Dijkgraaf and Vafa. Nevertheless, it has a simple form on the auxiliary Riemann surface of the matrix model. Thus the underlying geometry of the matrix model leads to a definite prescription for computing \rho_{GT}(\l), knowing \rho_{MM}(\l).Comment: 16 pages; v2. Further elaboration in Sec. 5 on the relation between gauge and matrix eigenvalue distributions, v3: Minor change

Spin polarisation by external magnetic fields, Aharonov-Bohm flux strings, and chiral symmetry breaking in QED3_3

In the first part, the induced vacuum spin around an Aharonov-Bohm flux string in massless three-dimensional QED is computed explicitly and the result is shown to agree with a general index theorem. A previous observation in the literature, that the presence of induced vacuum quantum numbers which are not periodic in the flux make an integral-flux AB string visible, is reinforced. In the second part, a recent discussion of chiral symmetry breaking by external magnetic fields in parity invariant QED$_3$ and its relation to the induced spin in parity non-invariant QED$_3$ is further elaborated. Finally other vacuum polarisation effects around flux tubes in different variants of QED, in three and four dimensions are mentioned.Comment: 20 page Latex fil

Guessing based on length functions

A guessing wiretapper's performance on a Shannon cipher system is analyzed for a source with memory. Close relationships between guessing functions and length functions are first established. Subsequently, asymptotically optimal encryption and attack strategies are identified and their performances analyzed for sources with memory. The performance metrics are exponents of guessing moments and probability of large deviations. The metrics are then characterized for unifilar sources. Universal asymptotically optimal encryption and attack strategies are also identified for unifilar sources. Guessing in the increasing order of Lempel-Ziv coding lengths is proposed for finite-state sources, and shown to be asymptotically optimal. Finally, competitive optimality properties of guessing in the increasing order of description lengths and Lempel-Ziv coding lengths are demonstrated.Comment: 16 pages, Submitted to IEEE Transactions on Information Theory, Special issue on Information Theoretic Security, Simplified proof of Proposition