scholarly journals The nth reduced BKP hierarchy, the string equation and BW 1+∞-constraints

1996 ◽  
Vol 44 (1-2) ◽  
pp. 185-206 ◽  
Author(s):  
Johan Van de Leur
Keyword(s):  
String Equation ◽  
Bkp Hierarchy

scholarly journals ON THE STRING EQUATION OF THE BKP HIERARCHY

2009 ◽  
Vol 24 (22) ◽  
pp. 4193-4208 ◽  
Author(s):  
HSIN-FU SHEN ◽  
MING-HSIEN TU
Keyword(s):  
Spectral Parameter ◽  
String Equation ◽  
Bkp Hierarchy

The Adler–Shiota–van Moerbeke formula is employed to derive the W-constraints for the p-reduced BKP hierarchy constrained by the string equation. We also provide the Grassmannian description of the string equation in terms of the spectral parameter.

scholarly journals ON p – q DUALITY AND EXPLICIT SOLUTIONS IN c ≤ 1 2D GRAVITY MODELS

1995 ◽  
Vol 10 (08) ◽  
pp. 1219-1236 ◽  
Author(s):  
S. KHARCHEV ◽  
A. MARSHAKOV
Keyword(s):  
String Theory ◽  
Exact Solutions ◽  
2D Gravity ◽  
Integral Formula ◽  
Integral Representations ◽  
Gravity Models ◽  
Explicit Solutions ◽  
String Equation ◽  
Duality Transformation

We study the role of integral representations in the description of nonperturbative solutions to c ≤ 1 string theory. A generic solution is determined by two functions, W(x) and Q(x), which behave at infinity like xp and xq respectively. The integral formula for arbitrary (p, q) models is derived, which explicitly realizes a duality transformation between (p, q) and (q, p) 2D gravity solutions. We also discuss the exact solutions to the string equation and reduction condition and present several explicit examples.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

scholarly journals M-BRANE MODELS AND LOOP SPACES

2012 ◽  
Vol 27 (20) ◽  
pp. 1230019 ◽  
Author(s):  
CHRISTIAN SÄMANN
Keyword(s):  
Loop Space ◽  
The Self ◽  
String Equation ◽  
Loop Spaces ◽  
Brane Model ◽  
Recent Developments ◽  
Brane Models ◽  
Space Approach

I review an extension of the ADHMN construction of monopoles to M-brane models. This extended construction gives a map from solutions to the Basu–Harvey equation to solutions to the self-dual string equation transgressed to loop space. Loop spaces appear in fact quite naturally in M-brane models. This is demonstrated by translating a recently proposed M5-brane model to loop space. Finally, I comment on some recent developments related to the loop space approach to M-brane models.

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