Comments on 1/16 BPS Quantum States and Classical Configurations

We formulate the problem of counting 1/16 BPS states of N = 4 Yang Mills theory as the enumeration of the local cohomology of an operator acting on holomorphic fields on C^2. We study aspects of the enumeration of this cohomology at finite N, especially for operators constructed only out of products of covariant derivatives of scalar fields, and compare our results to the states obtained from the quantization of giant gravitons and dual giants. We physically interpret the holomorphic fields that enter our conditions for supersymmetry semi-classically by deriving a set of Bogomolnyi equations for 1/16-BPS bosonic field configurations in N = 4 Yang Mills theory on R^4 with reality properties and boundary conditions appropriate to radial quantization. An arbitrary solution to these equations in the free theory is parameterized by holomorphic data on C^2 and lifts to a nearby solution of the interacting Bogomolnyi equations only when the constraints equivalent to Q cohomology are obeyed.Comment: 61 page

No Fermionic Wigs for BPS Attractors in 5 Dimensions

We analyze the fermionic wigging of 1/2-BPS (electric) extremal black hole attractors in N=2, D=5 ungauged Maxwell-Einstein supergravity theories, by exploiting anti-Killing spinors supersymmetry transformations. Regardless of the specific data of the real special geometry of the manifold defining the scalars of the vector multiplets, and differently from the D=4 case, we find that there are no corrections for the near--horizon attractor value of the scalar fields; an analogous result also holds for 1/2-BPS (magnetic) extremal black string. Thus, the attractor mechanism receives no fermionic corrections in D=5 (at least in the BPS sector).Comment: 24 pages, LaTeX2

Lower-dimensional pure-spinor superstrings

We study to what extent it is possible to generalise Berkovits' pure-spinor construction in d=10 to lower dimensions. Using a suitable definition of a ``pure'' spinor in d=4,6, we propose models analogous to the d=10 pure-spinor superstring in these dimensions. Similar models in d=2,3 are also briefly discussed.Comment: 17 page

Non-Critical Pure Spinor Superstrings

We construct non-critical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the non-critical pure spinor space, which is different from the ten-dimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the non-critical pure spinor type IIA superstring on AdS_4 with RR 4-form flux.Comment: LaTeX2e, 76 pages, no figures, JHEP style; v2: references and acknowledgments added, typos corrected; v3: typos corrected and minor changes to match published versio

Width and Partial Widths of Unstable Particles in the Light of the Nielsen Identities

Fundamental properties of unstable particles, including mass, width, and partial widths, are examined on the basis of the Nielsen identities (NI) that describe the gauge dependence of Green functions. In particular, we prove that the pole residues and associated definitions of branching ratios and partial widths are gauge independent to all orders. A simpler, previously discussed definition of branching ratios and partial widths is found to be gauge independent through next-to-next-to-leading order. It is then explained how it may be modified in order to extend the gauge independence to all orders. We also show that the physical scattering amplitude is the most general combination of self-energy, vertex, and box contributions that is gauge independent for arbitrary s, discuss the analytical properties of the NI functions, and exhibit explicitly their one-loop expressions in the Z-gamma sector of the Standard Model.Comment: 20 pages (Latex); minor changes included, accepted for publication in Phys. Rev.

Constrained Supermanifolds for AdS M-Theory Backgrounds

A long standing problem is the supergauge completion of AdS_4 x (G/H)_7 or AdS_5 x (G/H)_5 backgrounds which preserve less then maximal supersymmetry. In parallel with the supersolvable realization of the AdS_4 x S^7 background based on Kappa-symmetry, we develop a technique which amounts to solving the above-mentioned problem in a way useful for pure spinor quantization for supermembranes and superstrings. Instead of gauge fixing some of the superspace coordinates to zero, we impose an additional constraint on them reproducing the simplifications of the supersolvable representations. The constraints are quadratic, homogeneous, Sp(4,R)-covariant, and consistent from the quantum point of view in the pure spinor approach. Here we provide the geometrical solution which, in a subsequent work, will be applied to the membrane and the superstring sigma models.Comment: LaTex, 47 pages, no figure

Super D-branes from BRST Symmetry

Recently a new formalism has been developed for the covariant quantization of superstrings. We study properties of Dp-branes and p-branes in this new framework, focusing on two different topics: effective actions and boundary states for Dp-branes. We present a derivation of the Wess-Zumino terms for super (D)p-branes using BRST symmetry. To achieve this we derive the BRST symmetry for superbranes, starting from the approach with/without pure spinors, and completely characterize the WZ terms as elements of the BRST cohomology. We also develope the boundary state description of Dp-branes by analyzing the boundary conditions for open strings in the completely covariant (i.e., without pure spinors) BRST formulation.Comment: 31 pp; journal version, expended discussion of D-brane pure spinor constraints in Section 2.

Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground

By making an appropriate choice for gauge fixing kappa-symmetry we obtain a relatively simple form of the actions for a D=11 superparticle in AdS(4) x S(7)/Z_k, and for a D0-brane, fundamental string and D2-branes in the AdS(4) x CP(3) superbackground. They can be used to study various problems of string theory and the AdS4/CFT3 correspondence, especially in regions of the theory which are not reachable by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model. In particular, we present a simple form of the gauge-fixed superstring action in AdS(4) x CP(3) and briefly discuss issues of its T-dualization.Comment: 1+36 pages, v2,v3 clarifications and references adde

Width and Partial Widths of Unstable Particles

In the gauge theory context, a definition of branching ratios and partial widths of unstable particles is proposed that satisfies the basic principles of additivity and gauge independence. A simpler definition, similar to the conventional one, is examined in the Z^0-boson case. In order to establish contact with experiment, we show that it leads to a peak cross section that justifies the expression used by the LEP Electroweak Working Group through next-to-next-to-leading order, provided that the pole rather than the on-shell mass and width of the Z^0 boson are employed.Comment: 8 pages, LaTex, no figures, macros included, A more complete theoretical discussion and applications to the Z^0 peak cross section are include