Special Issue "Super Geometry for Super Strings"

A special issue of Universe (ISSN 2218-1997).

Deadline for manuscript submissions: closed (31 August 2018) | Viewed by 3990

Special Issue Editors

Prof. Dr. Sergio Luigi Cacciatori
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Guest Editor
Department of Science and High Technology, Università dell'Insubria, via Valleggio 11, 22100 Como, Italy
Interests: general relativity; black hole physics; quantum gravity; analogue gravity; string theory; branes and mirror symmetry; superstring amplitudes; mathematical aspects of string theory; M-theory; F-theory
Dr. Hervé Partouche
E-Mail Website
Guest Editor
Centre de Physique Théorique, Ecole Polytechnique, F-91128 Palaiseau CEDEX, France
Interests: string theory (compactification, 2D conformal field theory, cosmology, phenomenology, dualities, "geometric engineering", low energy effective description, strings at finite temperature); supergravity; supersymmetry; braneworlds; M-theory

Special Issue Information

Dear Colleagues,

In recent years, defining perturbative superstring theory at genus higher than two has gained a renewed interest. The success of the past twenty years, and efforts by D’Hoker and Phong (fom [1] to [2]) in computing the amplitudes for the case of genus two, based on the idea of parameterizing the supermoduli space of super Riemann surfaces in terms of a super period matrix, has given a boost to several researchers, both in theoretical physics and in algebraic geometry in exploring more deeply the subject. Indeed, naïve attempts in generalizing the genus two results to higher genus fail because the nontrivial geometrical properties of the supermoduli space, which at higher genus fails to be split ([3,4]).

The aim of this Special Issue is to collect, in a contained format, the general problem of formulating perturbative super string theory at any genus, the successes obtained up to now, both from the physical and the mathematical point of view, but also the numerous open problems and the strategies that are actually more or less adopted in order to attach a problem, which requires the efforts of both physicists and algebraic geometers [5].

Dr. Sergio Luigi Cacciatori
Dr. Hervé Partouche
Guest Editors

Manuscript Submission Information

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References

[1]. D’Hoker, E.; Phong, D.H. The geometry of string perturbation theory. Rev. Mod. Phys. 1988, 60, 917–1065.
[2]. D’Hoker, E.; Phong, D.H. Two-Loop Superstrings VII, Cohomology of Chiral Amplitudes. Nucl. Phys. B 2008, 804, 421–506.
[3]. Donagi, R.; Witten, E. Supermoduli Space Is Not Projected. 2013, arXiv:1304.7798.
[4]. Donagi, R.; Witten, E. Super Atiyah classes and obstructions to splitting of supermoduli space. 2014, arXiv:1404.6257.
[5]. Donagi, R.; Grushevsky, S.; Katz, S.; Witten, E. Supermoduli Workshop, New York, NY, USA, May 18–22, 2015.

Published Papers (3 papers)

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Research

Article
Non-Projected Supermanifolds and Embeddings in Super Grassmannians
Universe 2018, 4(11), 114; https://doi.org/10.3390/universe4110114 - 05 Nov 2018
Cited by 7 | Viewed by 1099
Abstract
In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results (L. Sergio et al., 2018), we study an explicit example of non-projected and non-projective supermanifold over the projective plane and show [...] Read more.
In this paper we give a brief account of the relations between non-projected supermanifolds and projectivity in supergeometry. Following the general results (L. Sergio et al., 2018), we study an explicit example of non-projected and non-projective supermanifold over the projective plane and show how to embed it into a super Grassmannian. The geometry of super Grassmannians is also reviewed in detail. Full article
(This article belongs to the Special Issue Super Geometry for Super Strings)
Article
String Sigma Models on Curved Supermanifolds
Universe 2018, 4(4), 60; https://doi.org/10.3390/universe4040060 - 24 Apr 2018
Cited by 2 | Viewed by 1213
Abstract
We use the techniques of integral forms to analyze the easiest example of two-dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D=2 supermanifold, and we show how to interpolate [...] Read more.
We use the techniques of integral forms to analyze the easiest example of two-dimensional sigma models on a supermanifold. We write the action as an integral of a top integral form over a D = 2 supermanifold, and we show how to interpolate between different superspace actions. Then, we consider curved supermanifolds, and we show that the definitions used for flat supermanifolds can also be used for curved supermanifolds. We prove it by first considering the case of a curved rigid supermanifold and then the case of a generic curved supermanifold described by a single superfield E. Full article
(This article belongs to the Special Issue Super Geometry for Super Strings)
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Article
Super Bundles
Universe 2018, 4(3), 46; https://doi.org/10.3390/universe4030046 - 01 Mar 2018
Cited by 6 | Viewed by 1223
Abstract
In this paper we give a brief account of the main aspects of the theory of associated and principal super bundles. As an application, we review the Borel-Weil-Bott Theorem in the super setting, and some results on projective embeddings of homogeneous spaces. Full article
(This article belongs to the Special Issue Super Geometry for Super Strings)
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