6971380
Effective Field Theory for Coherent Optical Pulse Propagation
Hidden nonabelian symmetries in nonlinear interactions of radiation with matter are clarified. In terms of a nonabelian potential variable, we construct an effective field theory of self-induced transparency, a phenomenon of lossless coherent pulse propagation, in association with Hermitian symmetric spaces $G/H$. Various new properties of self-induced transparency, e.g. soliton numbers, effective potential energy, gauge symmetry and discrete symmetries, modified pulse area, conserved $U(1)$-charge etc. are addressed and elaborated in the nondegenerate two-level case where $G/H = SU(2)/U(1)$. Using the $U(1)$-charge conservation, a new type of analysis on pulse stability is given which agrees with earlier numerical results.
15532318
Deformed minimal models and generalized Toda theory
Abstract We introduce a generalization of A r -type Toda theory based on a non-Abelian group G , which we call the ( A r , G )-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine ( A 1 , SU (2))-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator Φ (2,1) . We derive infinite conserved charges and soliton solutions from the Lax pair of the affine ( A 1 , SU (2))-Toda theory. Another type of integrable deformation which accounts for the Φ (3,1) -deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.
15297893
Possible tests of conformal turbulence through boundaries
Abstract We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities such as the energy power spectrum E ( k ) or the average velocity profiles. We propose that these effects can be used as a possible test of conformal turbulence in an experimental setting. We also study the periodic boundary conditions, i.e. turbulence on a torus geometry. The dependence of moduli parameter q appears explicitly in the one point functions in the theory, which can also be tested.
14536317
Solutions of conformal turbulence on a half plane
Abstract Exact solutions of conformal turbulence restricted to the upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tuning of coefficients. The simplest solution in our case is given by the minimal model of p = 2, q = 33 and moreover we find a fixed point of solutions when p , q become large.
14868745
Path integral bosonization of massive GNO fermions
We show the quantum equivalence between certain symmetric space sine-Gordon models and the massive free fermions. In the massless limit, these fermions reduce to the free fermions introduced by Goddard, Nahm and Olive (GNO) in association with symmetric spaces KG. A path integral formulation is given in terms of the Wess-Zumino-Witten action where the field variable g takes value in the orthogonal, unitary, and symplectic representations of the group G in the basis of the symmetric space. We show that, for example, such a path integral bosonization is possible when the symmetric spaces KG are SU(N) × SU(N)/SU(N); N ⩽ 3, Sp(2)/U(2) or SO(8)/U(4). We also address the relation between massive GNO fermions and the non-Abelian solitons, and explain the restriction imposed on the fermion mass matrix due to the integrability of the bosonic model.
120779082
Primary operators of coset conformal field theories
The nature of primary operators of coset conformal field theories is discussed. Some primary states of typical coset conformal field theory are explicitly calculated that have correct conformal dimensions and dynamics. The nature of modular invariant partition functions from the diagonal sum of absolute squares of characters of coset primary states is studied.
122640782
D3 + D6 solution and D4 + D6 solution
Abstract We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D =11 solutions (M3 branes and M4 branes with the Z N identifications in the transverse space) we obtain the D =10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D =10 along a circular direction of S 3 part of the transverse space. M3 brane solution leads to D =10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.