Superconformal Interpretation of BPS States in AdS Geometries

We carry out a general analysis of the representations of the superconformal algebras SU(2, 2/N), OSp(8/4, ), and OSp(8*/2N) and give their realization in superspace. We present a construction of their UIRs by multiplication of the different types of massless superfields (supersingletons). Particular attention is paid to the so-called short multiplets. Representations undergoing shortening have protected dimension and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.     

Knots,BPS States,and Algebraic Curves

We analyze relations between BPS degeneracies related to Labastida-Mariño-Ooguri-Vafa (LMOV) invariants and algebraic curves associated to knots. We introduce a new class of such curves, which we call extremal A-polynomials, discuss their special properties, and determine exact and asymptotic formulas for the corresponding (extremal) BPS degeneracies. These formulas lead to nontrivial integrality statements in number theory, as well as to an improved integrality conjecture, which is stronger than the known M-theory integrality predictions. Furthermore, we determine the BPS degeneracies encoded in augmentation polynomials and show their consistency with known colored HOMFLY polynomials. Finally, we consider refined BPS degeneracies for knots, determine them from the knowledge of super-A-polynomials, and verify their integrality. We illustrate our results with twist knots, torus knots, and various other knots with up to 10 crossings.     

Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions

In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kähler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers. The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the other hand, the pyramid partitions describe T ³ fixed points of the moduli space of a quiver quantum mechanics. This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system on the conifold and choose a particular set of FI parameters. The arrow structure of the dual quiver is confirmed by computation of the Ext group between the sheaves. We show that the superpotential and the stability condition of the dual quiver with this choice of the FI parameters give rise to the rules specifying pyramid partitions with length n ERC.     

Counting BPS operators in SYM

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.     

Modular Constraints on Calabi-Yau Compactifications

We derive global constraints on the non-BPS sector of supersymmetric 2d sigma-models whose target space is a Calabi-Yau manifold. When the total Hodge number of the Calabi-Yau threefold is sufficiently large, we show that there must be non-BPS primary states whose total conformal weights are less than 0.656. Moreover, the number of such primary states grows at least linearly in the total Hodge number. We discuss implications of these results for Calabi-Yau geometry.     

Neutral Calabi-Yau Structures on Kodaira Manifolds

We construct neutral Calabi-Yau metrics and hypersymplectic structures on some Kodaira manifolds. Our structures are symmetric with respect to the central tori.Partially supported by The European Contract HPRN-CT-2000-00101, MURST and GNSAGA (Indam) of ItalyPartially supported by The European Contract HPRN-CT-2000-00101Partially supported by NSF     

Conditionally Teleported States Using Optical Squeezers and Photon Counting

By virtue of the neat expression of the two-mode squeezing operator in the Einstein,Podolsky and Rosen entangled state representation,we provide a new approach for discussing the teleportation scheme using optical squeezers and photon counting devices.We derive the explicit form of the teleported states,so that the conditional property of teleportation and teleportation fidelity of this protocol can be seen more clearly.The derivation is concise.     

A remark on the scattering of BPS monopoles

It is shown that the classical dynamics of several slowly moving monopoles corresponds to a geodesic motion in the manifold of exact, static multi-monopole configurations.     

Duality Covariant Formulation of Extended Supergravity: Central Charges,BPS States and Black-Hole Entropy

In these lectures we give a geometrical formulation of N-extrended supergravities which generalizes N = 2 special geometry of N = 2 theories. In all these theories duality symmetries are related to the notion of “flat symplectic bundles” and central charges may be defined as “sections” over these bundles. Attractor points giving rise to “fixed scalars” of the horizon geometry and Bekenstein-Hawking entropy formula for extremal black-holes are discussed in some details.     

On the Constraints Defining BPS Monopoles

We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU(2) BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for constructing monopoles of arbitrary charge can be regarded as a special case of these. As an application, we study the spectral curve of the tetrahedrally symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to be modified. A particular 1-cycle on the spectral curve plays an important rôle in our analysis.     

Some exact results on the superpotential from Calabi-Yau compactifications

We prove that certain superpotential couplings in compactified string theories are given exactly by the values calculated at sigma-model tree level. In particular, the 27³ coupling in (2,2) compactifications is a coupling of this sort. We explicitly check our results by examining the couplings in an exactly soluble model proposed by Gepner as a particular point in the moduli space of (2,2) compactifications on Y_{4; 5}. We thus determine the exact values of the normalized 27³ couplings for any value of the radius of Y_{4; 5}.     

Superconformal Structures on Generalized Calabi-Yau Metric Manifolds

We construct an embedding of two commuting copies of the N = 2 superconformal vertex algebra in the space of global sections of the twisted chiral-anti-chiral de Rham complex of a generalized Calabi-Yau metric manifold, including the case when there is a non-trivial H-flux and non-vanishing dilaton. The 4 corresponding BRST charges are well defined on any generalized Kähler manifold. This allows one to consider the half-twisted model defining thus the chiral de Rham complex of a generalized Kähler manifold. The classical limit of this result allows one to recover the celebrated generalized Kähler identities as the degree zero part of an infinite dimensional Lie superalgebra attached to any generalized Kähler manifold. As a byproduct of our study we investigate the properties of generalized Calabi-Yau metric manifolds in the Lie algebroid setting.     

Comments on possible new three-generation Calabi-Yau manifolds

We present the observation that the new Calabi-Yau manifolds suggested by Aspinwall et al. and Candelas et al. do not admit the appropriate freely acting discrete symmetries needed to give to three generations.     

BPS equations and the stress tensor

We exploit the relationship between the space components T_ij$T_{ij}$ of the energy–momentum tensor and the supercurrent to discuss the connection between the BPS equations and the vanishing of the components of the stress tensor in various supersymmetric theories with solitons. Using the fact that certain combination of supercharges annihilate BPS states, we show that T_ij=0$T_{ij}=0$ for kinks, vortices and dyons, displaying the connection between supersymmetry and non-interacting BPS solitons.     

D-branes on Calabi-Yau spaces and their mirrors

We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms D-branes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calabi-Yau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as T-duality are also discussed.     

BPS states on non-commutative tori and duality

We study gauge theories on non-commutative tori. It has been proved that Morita equivalence of non-commutative tori leads to a physical equivalence ( ) of the corresponding gauge theories [Nucl. Phys. B 534 (1998) 720]. We calculate the energy spectrum of maximally supersymmetric BPS states in these theories and show that this spectrum agrees with the . The relation of our results with those of recent calculations is discussed.