scholarly journals D-instanton perturbation theory

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Perturbation Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Open String ◽  
Collective Coordinates ◽  
Zero Modes ◽  
World Volume ◽  
Infra Red ◽  
Gauge Fixing ◽  
Zero Momentum

Abstract D-instanton world-volume theory has open string zero modes describing collective coordinates of the instanton. The usual perturbative amplitudes in the D-instanton background suffer from infra-red divergences due to the presence of these zero modes, and the usual approach of analytic continuation in momenta does not work since all open string states on a D-instanton carry strictly zero momentum. String field theory is well-suited for tackling these issues. However we find a new subtlety due to the existence of additional zero modes in the ghost sector. This causes a breakdown of the Siegel gauge, but a different gauge fixing consistent with the BV formalism renders the perturbation theory finite and unambiguous. At each order, this produces extra contribution to the amplitude besides what is obtained from integration over the moduli space of Riemann surfaces.

BELAVIN-KNIZHNIK FORMULA FOR OPEN BOSONIC STRING

1989 ◽  
Vol 04 (04) ◽  
pp. 375-383
Author(s):  
F. ARDALAN ◽  
H. ARFAEI ◽  
A. SHAFII-DEHABAD
Keyword(s):  
Perturbation Theory ◽  
Partition Function ◽  
Holomorphic Function ◽  
Bosonic Strings ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Open String ◽  
Bosonic String ◽  
Period Matrix

We derive the analog of Belavin-Knizhnik formula for both orientable and nonorientable open bosonic strings. At the order 2g of perturbation theory, the open string partition function is given for orientable and non-orientable topologies as an integral over a subvariety of the moduli space of genus g Riemann surfaces. The integrand is the modulus of the holomorphic function of Belavin and Knizhnik multipied by ( det Im T)−13 where T is obtained from the period matrix.

scholarly journals Closed string deformations in open string field theory. Part II. Superstring

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Carlo Maccaferri ◽  
Jakub Vošmera
Keyword(s):  
Hilbert Space ◽  
Perturbation Theory ◽  
Hilbert Spaces ◽  
Source Term ◽  
Open String ◽  
Closed String ◽  
Gauge Invariant ◽  
Gauge Fixing ◽  
Invariant Coupling ◽  
String State

Abstract This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the A∞ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new A∞ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space.

scholarly journals CURVED D-BRANE GEOMETRY AND ZERO MODES

2001 ◽  
Vol 16 (01) ◽  
pp. 41-55
Author(s):  
SUPRIYA KAR
Keyword(s):  
Vital Role ◽  
Type I ◽  
Ultraviolet Divergence ◽  
Superstring Theory ◽  
Integral Formalism ◽  
Collective Coordinates ◽  
Zero Modes ◽  
Effective Dynamics ◽  
World Volume ◽  
Perturbative Corrections

We present a path integral formalism to review the effective dynamics of an arbitrary and curved Dirichlet p-brane (Dp-brane) in open bosonic string and subsequently in type I superstring theory. We obtain the perturbative corrections to the Dirac–Born–Infeld dynamics up to [Formula: see text] in the presence of an antisymmetric two-form B field. A part of the corrections can be seen to be associated with an ultraviolet divergence. Renormalization of the Dp-brane collective coordinates is performed to show that the residual corrections lead to a noncommutative description on the world volume. The Dp-brane modes are analyzed and we show that its zero modes play a vital role in noncommutative geometry. Our analysis facilitates the noncommutative world volume description for an arbitrary B field.

A Primer on Mapping Class Groups (PMS-49)

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Graduate Students ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Class Group ◽  
Mapping Class ◽  
Torelli Group ◽  
Surface Bundles ◽  
Surface Homeomorphisms ◽  
Low Dimensional

The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. It begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn–Nielsen–Baer–theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals Chiral perturbation theory for GR

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Kirill Krasnov ◽  
Yuri Shtanov
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation ◽  
Perturbative Calculation ◽  
New Formalism ◽  
Yang Mills ◽  
First Order ◽  
Starting Point ◽  
Gauge Fixing ◽  
New Perturbation ◽  
Effective Description

Abstract We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.

scholarly journals SELF-DUALITY OF SUPER D3-BRANE ACTION ON AdS5×S5 BACKGROUND

1999 ◽  
Vol 14 (05) ◽  
pp. 327-335 ◽  
Author(s):  
T. KIMURA
Keyword(s):  
Gauge Field ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Duality Transformation ◽  
Self Duality ◽  
World Volume ◽  
The World ◽  
Gauge Fixing ◽  
Necessary And Sufficient ◽  
Brane Action

We show that the super D3-brane action on AdS5×S5 background recently constructed by Metsaev and Tseytlin is exactly invariant under the combination of the electric–magnetic duality transformation of the world-volume gauge field and the SO(2) rotation of N=2 spinor coordinates. The action is shown to satisfy the Gaillard–Zumino duality condition, which is a necessary and sufficient condition for an action to be self-dual. Our proof needs no gauge fixing for the κ-symmetry.

Sign in / Sign up

Export Citation Format

Share Document