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S. Pacheva

Publications and source records attributed to S. Pacheva.

At least 19 recordsLinked to original sources
arXiv2007

Generalized Gauge Field Approach To Lightlike Branes

We propose a general action describing the dynamics of lightlike (LL) p-branes in any odd (p+1) world-volume dimensions. Next, we consider self-consistent coupling of \textsl{LL}-membranes (p=2) to D=4 Einstein-Maxwell system plus a D=4 three-index antisymmetric tensor gauge field. The LL-brane serves as a material and charge source for gravity and electromagnetism and, furthermore, it produces a dynamical space-varying cosmological constant. We present static spherically-symmetric solutions where the space-time consists of two regions with different black-hole-type geometries and different values for dynamically generated cosmological constant, separated by the LL-brane which "straddles" their common event horizon.

hep-th↗
arXiv2005

Weyl-Conformally-Invariant Lightlike p-Brane Theories: New Aspects in Black Hole Physics and Kaluza-Klein Dynamics

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In D=4 the WILL-membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on (``straddles'') the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps non-trivially around the compact (internal)dimensions and still describes massless mode dynamics in the non-compact (space-time) dimensions. Due to nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with non-trivial angular momentum, and with linear dependence between energy and angular momentum.

hep-th↗
arXiv2004

Proceedings to the 7th Workshop 'What Comes Beyond the Standard Models', 19. - 31. July 2004, Bled, Slovenia

1. Predictions for Four Generations of Quarks Suggested by the Approach Unifying Spins and Charges (M. Breskvar, J. Mravlje, N.Mankoc Borstnik), 2. No-scale Supergravity and the Multiple Point Principle (C.Froggatt, L.Laperashvili, R.Nevzorov, H.B.Nielsen), 3. The Two-Higgs Doublet Model and the Multiple Point Principle (C.Froggatt, L.Laperashvili, R.Nevzorov, H.B.Nielsen, M.Sher), 4. New Physics From a Dynamical Volume Element (E. Guendelman, A. Kaganovich, E. Nissimov and S. Pacheva), 5. Randomness in Random Dynamics (A. Kleppe), 6. An Example of Kaluza-Klein-like Theories Leading After Compactification to Massless Spinors Coupled to a Gauge Field-Derivations and Proofs (N. Mankoc Borstnik, H. B. Nielsen and D. Lukman), 7. Geometry Decides Gravity, Demanding General Relativity-it is Thus the Quantum Theory of Gravity (R. Mirman), 8. Physics Would Be Impossible in Any Dimension But 3+1 - There Could Be Only Empty Universes (R. Mirman),9. Conservation of Energy Prohibits Proton Decay (R. Mirman), 10. Approximate Solutions for the Higgs Masses and Couplings in the NMSSM (R. Nevzorov and D.J. Miller)

hep-ph↗
arXiv2004

Impact of Dynamical Tensions in Modified String and Brane Theories

First we briefly outline the general construction of Dp-brane models with dynamical tensions. We then proceed to a more detailed discussion of a modified string model where the string tension is related to the potential of (an external) world-sheet electric current. We show that cancellation of the pertinent conformal anomaly on the quantum level requires the dynamical string tension to be a square of a free massless world-sheet scalar field.

hep-th↗
arXiv2000

Loop-Algebra and Virasoro Symmetries of Integrable Hierarchies of KP Type

We propose a systematic treatment of symmetries of KP integrable systems, including constrained (reduced) KP models ${\sl cKP}_{R,M}$, and their multi-component (matrix) generalizations. Any such integrable hierarchy is shown to possess an additional $({\hat U}(1)\oplus{\hat {SL}}(M))_{+} \oplus ({\hat {SL}}(M+R))_{-}$ loop-algebra symmetry. Also we provide a systematic construction of the full algebra of Virasoro additional symmetries in the case of constrained KP models which requires a nontrivial modification of the known Orlov-Schulman construction for the general unconstrained KP hierarchy. Multi-component KP hierarchies are identified as ordinary (scalar) one-component KP hierarchies supplemented with the Cartan subalgebra of the additional symmetry algebra, which provides the basis of a new method for construction of soliton-like solutions. Davey-Stewartson and $N$-wave resonant systems arise as symmetry flows of ordinary ${\sl cKP}_{R,M}$ hierarchies.

nlin.SI↗
arXiv1998

Berezinian Construction of Super-Solitons in Supersymmetric Constrained KP Hierarchies

We consider a broad class of consistently reduced Manin-Radul supersymmetric KP hierarchies (MR-SKP) which are supersymmetric analogs of the ordinary bosonic constrained KP models. Compatibility of these reductions with the MR fermionic isospectral flows is achieved via appropriate modification of the latter preserving their (anti-)commutation algebra. Unlike the general unconstrained MR-SKP case, Darboux-Backlund transformations do preserve the fermionic isospectral flows of the reduced MR-SKP hierarchies. This allows for a systematic derivation of explicit Berezinian solutions for the super-tau-functions (super-solitons) for these models.

solv-int↗
arXiv1998

Supersymmetric KP Hierarchy: ``Ghost'' Symmetry Structure, Reductions and Darboux-Backlund Solutions

This paper studies Manin-Radul supersymmetric KP hierarchy (MR-SKP) in three related aspects: (i) We find an infinite set of additional (``ghost'') symmetry flows spanning the same (anti-)commutation algebra as the ordinary MR-SKP flows; (ii) The latter are used to construct consistent reductions of the initial unconstrained MR-SKP hierarchy which involves a nontrivial modification for the fermionic flows; (iii) For the simplest constrained MR-SKP hierarchy we show that the orbit of Darboux-Backlund transformations lies on a supersymmetric Toda lattice being a square-root of the standard one-dimensional Toda lattice, and also we find explicit Wronskian-ratio solutions for the super-tau function.

solv-int↗
arXiv1997

A New ``Dual'' Symmetry Structure of the KP Hierarchy

A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to a new double-KP hierarchy embedding ``ghost'' and original KP-type Lax hierarchies connected to each other via a ``duality'' mapping exchanging the isospectral and ``ghost'' ``times''. A new representation of 2D Toda lattice hierarchy as a special Darboux-Backlund orbit of the double-KP hierarchy is found and parametrized entirely in terms of (adjoint) eigenfunctions of the original KP subsystem.

solv-int↗
arXiv1997

Method of Squared Eigenfunction Potentials in Integrable Hierarchies of KP Type

The method of squared eigenfunction potentials (SEP) is developed systematically to describe and gain new information about Kadomtsev-Petviashvili (KP) hierarchy and its reductions. Interrelation to the tau-function method is discussed in detail. The principal result, which forms the basis of our SEP method, is the proof that any eigenfunction of the general KP hierarchy can be represented as a spectral integral over the Baker-Akhiezer (BA) wave function with a spectral density expressed in terms of SEP. In fact, the spectral representations of the (adjoint) BA functions can, in turn, be considered as defining equations for the KP hierarchy. The SEP method is subsequently used to show how the reduction of the full KP hierarchy to the constrained KP hierarchies can be given entirely in terms of linear constraint equations on the pertinent tau-functions. The concept of SEP turns out to be crucial in providing a description of constrained KP hierarchies in the language of universal Sato Grassmannian and finding the non-isospectral Virasoro symmetry generators acting on the underlying tau-functions. The SEP method is used to write down generalized binary Darboux-Backlund transformations for constrained KP hierarchies whose orbits are shown to correspond to a new Toda model on a square lattice. As a result, we obtain a series of new determinant solutions for the tau-functions generalizing the known Wronskian (multi-soliton) solutions. Finally, applications to random matrix models in condensed matter physics are briefly discussed.

solv-int↗
arXiv1996

Constrained KP Hierarchies: Additional Symmetries, Darboux-Bäcklund Solutions and Relations to Multi-Matrix Models

This paper provides a systematic description of the interplay between a specific class of reductions denoted as \cKPrm ($r,m \geq 1$) of the primary continuum integrable system -- the Kadomtsev-Petviashvili ({\sf KP}) hierarchy and discrete multi-matrix models. The relevant integrable \cKPrm structure is a generalization of the familiar $r$-reduction of the full {\sf KP} hierarchy to the $SL(r)$ generalized KdV hierarchy ${\sf cKP}_{r,0}$. The important feature of \cKPrm hierarchies is the presence of a discrete symmetry structure generated by successive Darboux-Bäcklund (DB) transformations. This symmetry allows for expressing the relevant tau-functions as Wronskians within a formalism which realizes the tau-functions as DB orbits of simple initial solutions. In particular, it is shown that any DB orbit of a ${\sf cKP}_{r,1}$ defines a generalized 2-dimensional Toda lattice structure. Furthermore, we consider the class of truncated {\sf KP} hierarchies ({\sl i.e.}, those defined via Wilson-Sato dressing operator with a finite truncated pseudo-differential series) and establish explicitly their close relationship with DB orbits of \cKPrm hierarchies. This construction is relevant for finding partition functions of the discrete multi-matrix models. The next important step involves the reformulation of the familiar non-isospectral additional symmetries of the full {\sf KP} hierarchy so that their action on \cKPrm hierarchies becomes consistent with the constraints of the reduction. Moreover, we show that the correct modified additional symmetries are compatible with the discrete DB symmetry on the \cKPrm DB orbits. The above technical arsenal is subsequently applied to obtain complete

hep-th↗
arXiv1996

Virasoro Symmetry of Constrained KP Hierarchies

Additional non-isospectral symmetries are formulated for the constrained Kadomtsev-Petviashvili (\cKP) integrable hierarchies. The problem of compatibility of additional symmetries with the underlying constraints is solved explicitly for the Virasoro part of the additional symmetry through appropriate modification of the standard additional-symmetry flows for the general (unconstrained) KP hierarchy. We also discuss the special case of \cKP --truncated KP hierarchies, obtained as Darboux-Bäcklund orbits of initial purely differential Lax operators. The latter give rise to Toda-lattice-like structures relevant for discrete (multi-)matrix models. Our construction establishes the condition for commutativity of the additional-symmetry flows with the discrete Darboux-Bäcklund transformations of \cKP hierarchies leading to a new derivation of the string-equation constraint in matrix models.

hep-th↗
arXiv1995

Constrained KP Hierarchies: Darboux-Bäcklund Solutions and Additional Symmetries

We illustrate the basic notions of {\em additional non-isospectral symmetries} and their interplay with the discrete {\em \DB transformations} of integrable systems at the instance of {\em constrained Kadomtsev-Petviashvili} (\cKP) integrable hierarchies. As a main application we present the solution of discrete multi-matrix string models in terms of Wronskian $\t$-functions of graded $SL(m,1)$ \cKP hierarchies.

solv-int↗
arXiv1995

On Integrable Models and their Interrelations

We present an elementary discussion of the Calogero-Moser model. This gives us an opportunity to illustrate basic concepts of the dynamical integrable models. Some ideas are also presented regarding interconnections between integrable models based on the relation established between the Calogero-Moser model and the truncated KP hierarchy of Burgers-Hopf type.

solv-int↗
arXiv1995

Darboux-Backlund Solutions of SL(p,q) KP-KdV Hierarchies, Constrained Generalized Toda Lattices, and Two-Matrix String Model

We present an unifying description of the graded $SL(p,q)$ KP-KdV hierarchies, including the Wronskian construction of their tau-functions as well as the coefficients of the pertinent Lax operators, obtained via successive applications of special Darboux-Bäcklund transformations. The emerging Darboux-Bäcklund structure is identified as a constrained generalized Toda lattice system relevant for the two-matrix string model. Also, the exact Wronskian solution for the two-matrix model partition function is found.

hep-th↗
arXiv1995

Volume-Preserving Diffeomorphisms' versus Local Gauge Symmetry

We present a new form of Quantum Electrodynamics where the photons are composites made out of zero-dimensional scalar ``primitives''. The rôle of the local gauge symmetry is taken over by an {\em infinite-dimensional global Noether symmetry} -- the group of volume-preserving (symplectic) diffeomorphisms of the target space of the scalar primitives. Similar construction is carried out for higher antisymmetric tensor gauge theories. Solutions of Maxwell's equations are automatically solutions of the new system. However, the latter possesses additional non-Maxwell solutions which display some interesting new effects: (a) a magneto-hydrodynamical analogy, (b) absence of electromagnetic self-energy for electron plane wave solutions, and (c) gauge invariant photon mass generation, where the generated mass is arbitrary.

hep-th↗
arXiv1994

Reduction of Toda Lattice Hierarchy to Generalized KdV Hierarchies and Two-Matrix Model

Toda lattice hierarchy and the associated matrix formulation of the $2M$-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which abelianize the second KP Hamiltonian structure, we are able to obtain an unified formalism for the reduced $SL(M+1,M-k)$-KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded $SL (M+1,M-k)$ matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free-field representations of the associated $W(M,M-k)$ Poisson bracket algebras generalizing the familiar nonlinear $W_{M+1}$-algebra. Discrete Bäcklund transformations for $SL(M+1,M-k)$-KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the $SL (M+1,1)$-KdV hierarchy.

hep-th↗