The hamiltonian structure of the “bosonic” and “fermionic” extensions of N=2 KdV hierarchy
Supersymmetry and Quantum Field Theory
ABSTRACT We apply a manifestly N=2 supersymmetric coset formalism to the “bosonic” and “fermionic... more ABSTRACT We apply a manifestly N=2 supersymmetric coset formalism to the “bosonic” and “fermionic” extensions of N=2 KdV hierarchy. We construct the second Hamiltonian structure. It contains the same number of currents as the “small” N=4 SCA but with reversed statistics for two of them, and it is non-local.
We construct the ghost number 9 three strings vertex for OSFT in the natural normal ordering. We ... more We construct the ghost number 9 three strings vertex for OSFT in the natural normal ordering. We find two versions, one with a ghost insertion at z = i and a twistconjugate one with insertion at z = −i. For this reason we call them midpoint vertices. We show that the relevant Neumann matrices commute among themselves and with the matrix G representing the operator K 1. We analyze the spectrum of the latter and find that beside a continuous spectrum there is a (so far ignored) discrete one. We are able to write spectral formulas for all the Neumann matrices involved and clarify the important role of the integration contour over the continuous spectrum. We then pass to examine the (ghost) wedge states. We compute the discrete and continuous eigenvalues of the corresponding Neumann matrices and show that they satisfy the appropriate recursion relations. Using these results we show that the formulas for our vertices correctly define the star product in that, starting from the data of two ghost number 0 wedge states, they allow us to reconstruct a ghost number 3 state which is the expected wedge state with the ghost insertion at the midpoint, according to the star recursion relation.
We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311... more We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311198, in the operator formulation of Vacuum String Field Theory. We derive the tachyon wave function and then analyze the higher level fluctuations. We show that the dressing is responsible for implementing the transversality condition on the massless vector. In order to consistently deal with the singular k 0 mode we introduce a string midpoint regulator and we show that it is possible to accommodate all the open string states among the solutions to the linearized equations of motion. We finally show how the dressing can give rise to the correct ratio between the energy density of the dressed sliver and the brane tension computed via the three-tachyons-coupling.
We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311... more We analyze the fluctuations of the dressed sliver solution found in a previous paper, hep-th/0311198, in the operator formulation of Vacuum String Field Theory. We derive the tachyon wave function and then analyze the higher level fluctuations. We show that the dressing is responsible for implementing the transversality condition on the massless vector. In order to consistently deal with the singular k 0 mode we introduce a string midpoint regulator and we show that it is possible to accommodate all the open string states among the solutions to the linearized equations of motion. We finally show how the dressing can give rise to the correct ratio between the energy density of the dressed sliver and the brane tension computed via the three-tachyons-coupling.
A manifestly N=2 supersymmetric coset formalism is applied to analyze the "fermionic" e... more A manifestly N=2 supersymmetric coset formalism is applied to analyze the "fermionic" extensions of N=2, a=4 and a=-2 KdV hierarchies. Both hierarchies can be obtained from a manifest N=2 coset construction. This coset is defined as the quotient of some local but nonlinear superalgebra by a Û (1) subalgebra. Three superextensions of N=2 KdV hierarchy are proposed, among which one seems to be entirely new.
We show that for general spherically symmetric configurations, contributions of broad class of gr... more We show that for general spherically symmetric configurations, contributions of broad class of gravitational and mixed gauge-gravitational Chern-Simons terms to the equations of motion vanish identically in D > 3 dimensions. This implies that such terms in the action do not affect Birkhoff's theorem or any previously known spherically symmetric solutions. Furthermore, we investigate the thermodynamical properties using the procedure described in an accompanying paper. We find that in D > 3 static spherically symmetric case Chern-Simons terms do not contribute to the entropy either. Moreover, if one requires only for the metric tensor to be spherically symmetric, letting other fields unrestricted, the results extend almost completely, with only one possible exception-Chern-Simons Lagrangian terms in which the gravitational part is just the n = 2 irreducible gravitational Chern-Simons term.
This paper deals with the classification of spinor fields according to the bilinear covariants in... more This paper deals with the classification of spinor fields according to the bilinear covariants in 7 dimensions. The previously investigated Riemannian case is characterized by either one spinor field class, in the real case of Majorana spinors, or three non-trivial classes in the most general complex case. In this paper we show that by imposing appropriate conditions on spinor fields in 7d manifolds with Lorentzian metric, the formerly obtained obstructions for new classes of spinor fields can be circumvented. New spinor fields classes are then explicitly constructed. In particular, on 7-manifolds with asymptotically flat black hole background, these spinors can define a generalized current density which further defines a time Killing vector at the spatial infinity.
The Sugawara construction on genus-< i> g</i> Riemann surfaces
Physics Letters B, 1988
... One finds (33) (34) yi.8-i =gl2 - 1&amp;amp;gt; ni Ai=l(.iAn&amp;amp;gt; ~i=vnU%n It ... more ... One finds (33) (34) yi.8-i =gl2 - 1&amp;amp;gt; ni Ai=l(.iAn&amp;amp;gt; ~i=vnU%n It is easy to check that Jul 2 n= I ni f ConAi :A0 n,&amp;amp;gt;i-g12, =0 n&amp;amp;lt;ig/2, Pn 2oifAn(T)i:7O n,&amp;amp;lt;ig/2, =0 n&amp;amp;gt;ig/2. and it&amp;amp;quot;v8;, v;,~cm=8. With the help of these bases it is easy, though lenghty, to restrict the calculation to the circle ...
In this paper the subject of the BRST symmetry representation by means of superfields is resumed ... more In this paper the subject of the BRST symmetry representation by means of superfields is resumed and extended to N = 1 supersymmetric gauge theories. Then a new extension to diffeomorphisms is presented. Finally some speculations of a possible global representation of BRST symmetric theories by means of non-trivial supermanifolds are outlined.
We introduce the supersymmetric version of YM-like theories with infinitely many spin fields in f... more We introduce the supersymmetric version of YM-like theories with infinitely many spin fields in four dimensions. The construction is carried out via the superfield method. The surprising feature of these models is that they describe, in particular, gauge and gravity in a supersymmetric form, with no need for supergravity.
Proceedings of Third International Satellite Conference on Mathematical Methods in Physics — PoS(ICMP 2013)
This is a short introduction to open string field theory. Its purpose is to allow the reader to u... more This is a short introduction to open string field theory. Its purpose is to allow the reader to understand and appreciate the recently found analytic solutions of the equation of motion of the theory.
Some recent events have brought to the attention of the general public the issue of free access t... more Some recent events have brought to the attention of the general public the issue of free access to scientific information. On many occasions basic scientific information has been said to be constantly available to scientists. In truth, a group of scientists (those who live in the developing countries) have long remained on the fringes of the international research community and in part still are, mainly because of the existing difficulties in accessing scientific publications. However, this fact has never been as blatant as it was with the Human Genome Project. Indeed, the project saw an attempt to conceal and privatize the results of advanced basic research. On that occasion, the fear of a private exploitation of scientific results became a real threat.
Proceedings of 5th International School on Field Theory and Gravitation — PoS(ISFTG)
We review the calculation of the Hawking radiation in a Kerr black hole via the trace anomaly or ... more We review the calculation of the Hawking radiation in a Kerr black hole via the trace anomaly or the diff anomaly method. These methods account for the integrated radiation. But in order to describe the full Planckian spectrum of the Hawking radiation one needs to introduce higher spin currents. We show that the latter describe the higher moments of the Hawking radiation. This result is related to the appearance of higher order Schwarzian derivatives in the conformal transformation laws of these currents. We show that one can construct covariant higher spin currents and that such currents are covariantly conserved. In other words there are no anomalies in currents with spin higher than two. The higher spin currents form a W 1+∞ algebra. We show that this algebraic structure is at the root of their predictivity and in accordance with the no hairs theorem. This hints at the existence of a symmetry larger than the conformal one in the near horizon region of a black hole.
Proceedings of 5th International School on Field Theory and Gravitation — PoS(ISFTG)
This is short review of tachyon condensation and open string field theory. After a brief introduc... more This is short review of tachyon condensation and open string field theory. After a brief introduction to open string theory, the SFT action is introduced and illustrated. Next comes tachyon condensation in the level truncation approach, which introduces the main topic: the description of the analytic solution and the proof of the first two conjectures by Sen. The third conjecture is discussed in the framework of vacuum SFT. Finally the subject of open-closed string duality is tackled by commenting about an attempt at showing a more explicit connection between open and closed strings.
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Papers by L. Bonora