scholarly journals Integrable deformation of ℂPn and generalised Kähler geometry

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Saskia Demulder ◽  
Falk Hassler ◽  
Giacomo Piccinini ◽  
Daniel C. Thompson
Keyword(s):  
Target Space ◽  
Chiral Model ◽  
Kahler Geometry ◽  
Quotient Spaces ◽  
Integrable Deformation ◽  
Hermitian Geometry ◽  
Integrable Deformations ◽  
Kähler Potential ◽  
Complex Projective ◽  
Two Parameter

Abstract We build on the results of [1] for generalised frame fields on generalised quotient spaces and study integrable deformations for ℂPn. In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle. The second parameter can however be removed via a diffeomorphism, which we construct explicitly, in accordance with the results stemming from a thorough integrability analysis we carry out. We also elucidate how the deformed target space can be seen as an instance of generalised Kähler, or equivalently bi-Hermitian, geometry. In this respect, we find the generic form of the pure spinors for ℂPn and the explicit expression for the generalised Kähler potential for n = 1, 2.

scholarly journals ON TARGET SPACE DUALITY IN p-BRANES

1995 ◽  
Vol 10 (05) ◽  
pp. 441-450 ◽  
Author(s):  
R. PERCACCI ◽  
E. SEZGIN
Keyword(s):  
Dimensional Space ◽  
Target Space ◽  
Field Equations ◽  
Parameter Group ◽  
Duality Transformations ◽  
World Volume ◽  
The World ◽  
Dimensional Space Time ◽  
Background Fields ◽  
Two Parameter

We study the target space duality transformations in p-branes as transformations which mix the world volume field equations with Bianchi identities. We consider an (m+p+1)-dimensional space-time with p+1 dimensions compactified, and a particular form of the background fields. We find that while a GL (2) = SL (2) × R group is realized when m = 0, only a two-parameter group is realized when m > 0.

scholarly journals On the integrable deformations of a system related to the motion of two vortices in an ideal incompressible fluid

2019 ◽  
Vol 29 ◽  
pp. 01015 ◽  
Author(s):  
Cristian Lăzureanu ◽  
Ciprian Hedrea ◽  
Camelia Petrişor
Keyword(s):  
Incompressible Fluid ◽  
Mechanical System ◽  
Integrable Systems ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Ideal Incompressible Fluid ◽  
First Integrals ◽  
Integrable Deformation ◽  
Integrable Deformations ◽  
The Given

Altering the first integrals of an integrable system integrable deformations of the given system are obtained. These integrable deformations are also integrable systems, and they generalize the initial system. In this paper we give a method to construct integrable deformations of maximally superintegrable Hamiltonian mechanical systems with two degrees of freedom. An integrable deformation of a maximally superintegrable Hamiltonian mechanical system preserves the number of first integrals, but is not a Hamiltonian mechanical system, generally. We construct integrable deformations of the maximally superintegrable Hamiltonian mechanical system that describes the motion of two vortices in an ideal incompressible fluid, and we show that some of these integrable deformations are Hamiltonian mechanical systems too.

INTEGRABLE DEFORMATIONS OF THE NONUNITARY MINIMAL CONFORMAL MODEL ℳ3,5

1992 ◽  
Vol 07 (20) ◽  
pp. 5027-5044 ◽  
Author(s):  
G. MUSSARDO
Keyword(s):  
Field Theories ◽  
Conformal Space ◽  
One Dimensional ◽  
Conformal Model ◽  
Integrable Deformation ◽  
Anomalous Dimensions ◽  
Integrable Deformations ◽  
Scaling Region ◽  
The One ◽  
Space Approach

The scaling region of the nonunitary minimal conformal model M3,5 is described by three different integrable massive field theories. We propose the scattering theory for the integrable deformation of M3,5 by the field ψ with anomalous dimensions [Formula: see text]. The spectrum of this theory is confirmed by the Truncation Conformal Space Approach. We also consider the thermodynamics of the one-dimensional quantum system defined by the transfer matrix relative to the deformation of M3,5 by the field φ with anomalous dimensions [Formula: see text]. This deformation drives the original conformal model into a region of the phase diagram where there are plasma oscillations.

scholarly journals General Static N=2 Black Holes

1997 ◽  
Vol 12 (34) ◽  
pp. 2585-2590 ◽  
Author(s):  
W. A. Sabra
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Arbitrary Number ◽  
Harmonic Functions ◽  
Kahler Geometry ◽  
Kähler Potential ◽  
Black Hole Solutions

We find general static BPS black hole solutions for general N=2, d=4 supergravity theories with an arbitrary number of vector multiplets. These solutions are completely specified by the Kähler potential of the underlying special Kähler geometry and a set of constrained harmonic functions.

scholarly journals Inflation in Supergravity from Field Redefinitions

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 806
Author(s):  
Michał Artymowski ◽  
Ido Ben-Dayan
Keyword(s):  
Infinite Number ◽  
Model Building ◽  
Kahler Geometry ◽  
Bell Curve ◽  
Particle Phenomenology ◽  
Curve Model ◽  
Kähler Potential ◽  
O 10 ◽  
Inflationary Models ◽  
Field Redefinition

Supergravity (SUGRA) theories are specified by a few functions, most notably the real Kähler function denoted by G ( T i , T ¯ i ) = K + log | W | 2 , where K is a real Kähler potential, and W is a holomorphic superpotential. A field redefinition T i → f 1 ( T i ) changes neither the theory nor the Kähler geometry. Similarly, the Kähler transformation, K → K + f 2 + f ¯ 2 , W → e − f 2 W where f 2 is holomorphic and leaves G and hence the theory and the geometry invariant. However, if we perform a field redefinition only in K ( T i , T ¯ i ) → K ( f ( T i ) , f ( T ¯ i ) ) , while keeping the same superpotential W ( T i ) , we get a different theory, as G is not invariant under such a transformation while maintaining the same Kähler geometry. This freedom of choosing f ( T i ) allows construction of an infinite number of new theories given a fixed Kähler geometry and a predetermined superpotential W. Our construction generalizes previous ones that were limited by the holomorphic property of W. In particular, it allows for novel inflationary SUGRA models and particle phenomenology model building, where the different models correspond to different choices of field redefinitions. We demonstrate this possibility by constructing several prototypes of inflationary models (hilltop, Starobinsky-like, plateau, log-squared and bell-curve) all in flat Kähler geometry and an originally renormalizable superpotential W. The models are in accord with current observations and predict r ∈ [ 10 − 6 , 0.06 ] spanning several decades that can be easily obtained. In the bell-curve model, there also exists a built-in gravitational reheating mechanism with T R ∼ O ( 10 7 G e V ) .

SYMMETRY, INTEGRABILITY AND DEFORMATIONS OF LONG-RANGE INTERACTING HAMILTONIANS

1999 ◽  
Vol 13 (24n25) ◽  
pp. 2903-2908 ◽  
Author(s):  
ANGEL BALLESTEROS
Keyword(s):  
Long Range ◽  
Hamiltonian Systems ◽  
Quantum Algebra ◽  
Complete Integrability ◽  
Quantum Algebras ◽  
R Matrix ◽  
Completely Integrable ◽  
Integrable Deformation ◽  
Coalgebra Structure ◽  
Integrable Deformations

The notion of coalgebra symmetry in Hamiltonian systems is analysed. It is shown how the complete integrability of some long-range interacting Hamiltonians can be extracted from their associated coalgebra structure with no use of a quantum R-matrix. Within this framework, integrable deformations can be considered as direct consequences of the introduction of coalgebra deformations (quantum algebras). As an example, the Gaudin magnet is derived from a sl(2) coalgebra, and a completely integrable deformation of this Hamiltonian is obtained through a twisted gl(2) quantum algebra.

scholarly journals Poisson-Lie T-duality of WZW model via current algebra deformation

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Francesco Bascone ◽  
Franco Pezzella ◽  
Patrizia Vitale
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Current Algebra ◽  
Degrees Of Freedom ◽  
Target Space ◽  
Moody Algebra ◽  
Hamiltonian Description ◽  
Direct Sum ◽  
Group Manifold ◽  
Two Parameter

Abstract Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of SU(2) as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $$ \mathfrak{su}(2)\left(\mathrm{\mathbb{R}}\right)\overset{\cdot }{\oplus}\mathfrak{a} $$ su 2 ℝ ⊕ ⋅ a , to the fully semisimple Kac-Moody algebra $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{C}}\right)\left(\mathrm{\mathbb{R}}\right) $$ sl 2 ℂ ℝ . A two-parameter family of models with SL(2, ℂ) as target phase space is obtained so that Poisson-Lie T-duality is realised as an O(3, 3) rotation in the phase space. The dual family shares the same phase space but its configuration space is SB(2, ℂ), the Poisson-Lie dual of the group SU(2). A parent action with doubled degrees of freedom on SL(2, ℂ) is defined, together with its Hamiltonian description.

scholarly journals Stability and Energy-Casimir Mapping for Integrable Deformations of the Kermack-McKendrick System

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Cristian Lăzureanu ◽  
Camelia Petrişor
Keyword(s):  
Integrable Systems ◽  
Equilibrium Points ◽  
Poisson System ◽  
Poisson Structures ◽  
Integrable Deformation ◽  
Constants Of Motion ◽  
Integrable Deformations ◽  
Dynamical Properties ◽  
The Stability ◽  
Mckendrick Model

Integrable deformations of a Hamilton-Poisson system can be obtained altering its constants of motion. These deformations are integrable systems that can have various dynamical properties. In this paper, we give integrable deformations of the Kermack-McKendrick model for epidemics, and we analyze a particular integrable deformation. More precisely, we point out two Poisson structures that lead to infinitely many Hamilton-Poisson realizations of the considered system. Furthermore, we study the stability of the equilibrium points, we give the image of the energy-Casimir mapping, and we point out some of its properties.

scholarly journals On the Integrable Deformations of the Maximally Superintegrable Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1000
Author(s):  
Cristian Lăzureanu
Keyword(s):  
Differential Equations ◽  
Arbitrary System ◽  
Superintegrable System ◽  
First Order ◽  
Integrable Deformation ◽  
Superintegrable Systems ◽  
Constants Of Motion ◽  
Integrable Deformations ◽  
Autonomous Differential Equations ◽  
New System

In this paper, we present the integrable deformations method for a maximally superintegrable system. We alter the constants of motion, and using these new functions, we construct a new system which is an integrable deformation of the initial system. In this manner, new maximally superintegrable systems are obtained. We also consider the particular case of Hamiltonian mechanical systems. In addition, we use this method to construct some deformations of an arbitrary system of first-order autonomous differential equations.

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