FUNCTIONAL INTEGRAL METHODS FOR FERMIONIC STRING AND SUPER RIEMANN SURFACES

1989 ◽  
Vol 04 (09) ◽  
pp. 2283-2315 ◽  
Author(s):  
KEN-JI HAMADA ◽  
MASARU TAKAO
Keyword(s):  
Light Cone ◽  
Riemann Surfaces ◽  
Functional Integral ◽  
Light Cone Gauge ◽  
Spin Structures ◽  
Integral Methods ◽  
Integral Measure ◽  
Fermionic String ◽  
Super Riemann Surfaces ◽  
The One

We investigate the light-cone gauge formulation of fermionic string of Mandelstam in a superspace. To formulate the fermionic string in a superspace, we use the theory of super Riemann surfaces (SRS). We define the Neumann functions and the Mandelstam mappings in a superspace by means of the so-called Abelian differentials of the first and the third kinds on SRS. In the super Schottky parametrization of SRS these superdifferentials are constructed at the multiloop level. The functional integral measure of a super light-cone diagram, which consists of 6g−6+2N even moduli parameters and 4g−4+2N odd ones, are specified in our formulation. In one-loop case with even spin structures we explicitly evaluate the superdeterminants on the super light-cone diagrams and calculate the one-loop amplitudes with N massless vector states. It is shown that the result is written in the form of a correlation function of the vertex operators. Furthermore, we evaluate the 3- and 4-particle amplitudes explicitly, which agree exactly with those calculated in the Green-Schwarz formulation.

SOME REMARKS CONCERNING THE FINITENESS OF N=4 SUPERSYMMETRIC YANG MILLS THEORIES

1988 ◽  
Vol 03 (01) ◽  
pp. 65-70 ◽  
Author(s):  
A. Bassetto ◽  
M. Dalbosco
Keyword(s):  
Light Cone ◽  
Green Functions ◽  
Loop Order ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Loop Level ◽  
Recent Treatment ◽  
The One

We carefully discuss the finiteness of SUSY YM N=4 in the light cone gauge, first at the one loop level by directly exhibiting the relevant terms of the lowest order Green functions and then at any loop order by using a recent treatment of the renormalization of general Yang-Mills theories in the light cone gauge. We point out the existence of a set of divergent Green functions which however do not contribute to observable quantities, thereby recovering consistency with formulations in other gauges.

SPIN STRUCTURES IN N=2 SUPER RIEMANN SURFACES OF GENUS 1

1989 ◽  
Vol 04 (11) ◽  
pp. 2779-2787
Author(s):  
Y.S. MYUNG
Keyword(s):  
Riemann Surfaces ◽  
Spin Structures ◽  
Super Riemann Surfaces

We clarify the spin structures in N=2 Super Riemann Surfaces of Genus 1 (N=2 Supertorus).

CHIRAL SUPERCONDUCTING MEMBRANES

2002 ◽  
Vol 17 (01) ◽  
pp. 73-87 ◽  
Author(s):  
RUBÉN CORDERO ◽  
EFRAÍN ROJAS
Keyword(s):  
Light Cone ◽  
Domain Walls ◽  
String Model ◽  
Point Of View ◽  
Lagrangian Description ◽  
Geometrical Approach ◽  
Light Cone Gauge ◽  
The One

We develop the dynamics of the chiral superconducting membranes (with null current) in an alternative geometrical approach either making a Lagrangian description and a Hamiltonian point of view. Besides this, we show the equivalence of the resulting descriptions to the one known Dirac–Nambu–Goto (DNG) case. Integrability for chiral string model is obtained using a proposed light-cone gauge. In a similar way, domain walls are integrated by means of a simple ansatz. We compare the results with recent works that appeared in the literature.

scholarly journals JT supergravity and Brezin-Gross-Witten tau-function

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Kazumi Okuyama ◽  
Kazuhiro Sakai
Keyword(s):  
Riemann Surfaces ◽  
Free Energies ◽  
Point Function ◽  
Tau Function ◽  
Kdv Hierarchy ◽  
The Matrix ◽  
Higher Genus ◽  
Super Riemann Surfaces ◽  
The One ◽  
Thermal Correlation

Abstract We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli space of super Riemann surfaces, which is characterized by the Brezin-Gross-Witten (BGW) tau-function of the KdV hierarchy. We find that the matrix model of JT supergravity is a special case of the BGW model with infinite number of couplings turned on in a specific way, by analogy with the relation between bosonic JT gravity and the Kontsevich-Witten (KW) model. We compute the genus expansion of the one-point function of JT supergravity and study its low-temperature behavior. In particular, we propose a non-perturbative completion of the one-point function in the Bessel case where all couplings in the BGW model are set to zero. We also investigate the free energy and correlators when the Ramond-Ramond flux is large. We find that by defining a suitable basis higher genus free energies are written exactly in the same form as those of the KW model, up to the constant terms coming from the volume of the unitary group. This implies that the constitutive relation of the KW model is universal to the tau-function of the KdV hierarchy.

EXPLICIT EVALUATION OF COVARIANT ONE-LOOP FOUR-POINT AMPLITUDE FOR OPEN FERMIONIC STRING

1987 ◽  
Vol 02 (03) ◽  
pp. 221-227 ◽  
Author(s):  
HISASHI YAMAMOTO ◽  
NAOHITO NAKAZAWA
Keyword(s):  
Light Cone ◽  
Type I ◽  
Superstring Theory ◽  
Operator Formalism ◽  
New Formalism ◽  
Explicit Evaluation ◽  
Fermionic String ◽  
Loop Amplitude ◽  
The One ◽  
Point Amplitude

We carry out the explicit evaluation of the covariant one-loop amplitude with four massless external bosons for open fermionic string by the operator formalism. The resulting expression of the amplitude completely coincides with that of the light-cone new formalism for type-I superstring theory in both the non-regularized and regularized schemes, giving an explicit demonstration for the one-loop equivalence of the old and new formalisms for the open superstring theory at the four-point interacting level.

scholarly journals THERMAL D-BRANE BOUNDARY STATES FROM TYPE IIB GREEN–SCHWARZ SUPERSTRING IN pp-WAVE BACKGROUND

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4485-4507 ◽  
Author(s):  
ION V. VANCEA
Keyword(s):  
Light Cone ◽  
Canonical Ensemble ◽  
Flat Space ◽  
Total System ◽  
Light Cone Gauge ◽  
Expectation Value ◽  
Boundary State ◽  
Boundary States ◽  
Pp Wave ◽  
The One

We construct the thermal boundary states from the type IIB Green–Schwarz superstring in pp-wave background in the light-cone gauge. The superstring is treated in the canonical ensemble and in the TFD formalism which is appropriate to discuss canonically quantized systems. The thermal boundary states are obtained by thermalizing the total boundary states which are the boundary states of the total system that is composed by the superstring modes and the corresponding thermal reservoir modes. That analysis is similar to the one in the flat space–time case.67 However, there are some subtleties concerning the construction of the total string which are discussed. Next, we compute the entropy of thermal boundary state which is defined as the expectation value of the superstring entropy operator in the thermal boundary state.

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