Superloop Equations and Two-Dimensional Supergravity

Álvarez‐Gaumé, Luis; Itoyama, H.; Mañes, Juan L.; Zadra, Ayrton

doi:10.1142/s0217751x92002441

Cited by 75 publications

(155 citation statements)

References 19 publications

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“…Therefore, substituting the first term in the anti-commutator in (242) with the expression (246) we conclude that for fermionic SKP (R; 1,0) hierarchies (245) (248) which is not equal to ± ( L 2n−1 ) − − X 2n−1 due to the opposite signs in front of both sums in (248). Therefore, fermionic isospectral flows D n are preserved under first type of super-DB transformations only for the subclass SKP (R;1,0) (245) of fermionic constrained super-KP hierarchies.…”

Section: Darboux-bäcklund Transformations For Constrained Super-kp Himentioning

confidence: 99%

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Symmetries of supersymmetric integrable hierarchies of KP type

Nissimov

Pacheva

2002

Journal of Mathematical Physics

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This paper is devoted to the systematic study of additional (non-isospectral) symmetries of constrained (reduced) supersymmetric integrable hierarchies of KP type -the so called SKP (R;MB ,MF ) models. The latter are supersymmetric extensions of ordinary constrained KP hierarchies which contain as special cases basic integrable systems such as (m)KdV, AKNS, FordyKulish, Yajima-Oikawa etc.. As a first main result it is shown that any SKP (R;MB ,MF ) hierarchy possesses two different mutually (anti-)commuting types of superloop superalgebra additional symmetries corresponding to the positive-grade and negative-grade parts of certain superloop superalgebras. The second main result is the systematic construction of the full algebra of additional Virasoro symmetries of SKP (R;MB ,MF ) hierarchies, which requires non-trivial modifications of the Virasoro flows known from the general case of unconstrained Manin-Radul super-KP hierarchies (the latter flows do not define symmetries for constrained SKP (R;MB ,MF ) hierarchies). As a third main result we provide systematic construction of the supersymmetric analogues of multi-component (matrix) KP hierarchies and show that the latter contain among others the supersymmetric version of Davey-Stewartson system. Finally, we present an explicit derivation of the general Darboux-Bäcklund solutions for the SKP (R;MB ,MF ) super-tau functions (supersymmetric "soliton"-like solutions) which preserve the additional (non-isospectral) symmetries.

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Section: Darboux-bäcklund Transformations For Constrained Super-kp Himentioning

confidence: 99%

“…(120)- (127). We take for convenience the following two mutually (anti-)commuting infinite sets of Manin-Radul-like flows: ∂/∂t n , D n (the original MR-SKP isospectral flows) and ∂/∂t n ≡ −∂/∂ (1) t n , (1) D n (recall ∂/∂t n = ∂/∂…”

Section: -(127) N -Component Constrained Super-kp Hierarchymentioning

confidence: 99%

Symmetries of supersymmetric integrable hierarchies of KP type

Nissimov

Pacheva

2002

Journal of Mathematical Physics

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“…[4]. The equation (18) is easily integrated and its unique solution (up to a multiplicative constant) is…”

Section: #1mentioning

confidence: 99%

“…As expounded in ref. [4], the guiding principle is the super-Virasoro structure of the partition function. Let us consider a super-pair of N × N hermitian matrix (Φ, Θ), whose matrix elements φ ij , θ ij 1 ≤ i, j ≤ N are Grassmann even and odd variables respectively.…”

mentioning

confidence: 99%

Matrix model with superconformal symmetry

Takama

1992

Physics Letters B

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“…In this paper, we will carry out this procedure in depth at the (m+1, m) critical point realized by the symmetric potential of the two-matrix model. 4 Here κ ≡ 1 N a 2+1/m .…”

Section: Introduction and Conclusionmentioning

confidence: 99%

Macroscopic n-loop amplitude for minimal models coupled to two-dimensional gravity. Fusion rules and interactions

Anazawa¹,

Itoyama²

1996

Nuclear Physics B

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We investigate the structure of the macroscopic n-loop amplitude obtained from the two-matrix model at the unitary minimal critical point (m+1, m). We derive a general formula for the n-resolvent correlator at the continuum planar limit whose inverse Laplace transform provides the amplitude in terms of the boundary lengths ℓ i and the renormalized cosmological constant t. The amplitude is found to contain a term consisting of ∂ ∂t n−3 multiplied by the product of modified Bessel functions summed over their degrees which conform to the fusion rules and the crossing symmetry. This is found to be supplemented by an increasing number of other terms with n which represent residual interactions of loops. We reveal the nature of these interactions by explicitly determining them as the convolution of modified Bessel functions and their derivatives for the case n = 4 and the case n = 5. We derive a set of recursion relations which relate the terms in the n-resolvents to those in the (n − 1)-resolvents.

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Superloop Equations and Two-Dimensional Supergravity

Cited by 75 publications

References 19 publications

Symmetries of supersymmetric integrable hierarchies of KP type

Symmetries of supersymmetric integrable hierarchies of KP type

Matrix model with superconformal symmetry

Macroscopic n-loop amplitude for minimal models coupled to two-dimensional gravity. Fusion rules and interactions

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