The branching rules of conformal embeddings

After recalling the main properties of a conformal embedding of Lie algebrasgp, which is defined by the equality of the Sugawara central charges on both sides, we launch a systematic study of their branching rules. The bulk of the paper is devoted to the proof of a general formula in the casesu(mn) ₁su(m) _nsu(n) _m. At the end we give some applications to the construction of modular invariant partition functions.     

Branching rules and replicating representations

The problem of finding irreducible representations of a simple Lie group that decompose into just pure replications of a representation of a subgroup is considered. Replications involving tensor representations of the orthogonal groups are studied in detail using counting groups whose representation dimensions correspond to branching multiplicities. Replications involving spinor and mixed tensor representations are briefly considered.     

On new conformal field theories with affine fusion rules

Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have extended W algebras which are close analogues of affine algebras. Exact character formulae are given, and the realizations are shown to be full-fledged unitary conformal field theories.     

Truncated conformal space at , nonlinear integral equation and quantization rules for multi-soliton states

We develop truncated conformal space (TCS) technique for perturbations of conformal field theories. We use it to give the first numerical evidence of the validity of the non-linear integral equation (NLIE) derived from light-cone lattice regularization at intermediate scales. A controversy on the quantization of Bethe states is solved by this numerical comparison and by using the locality principle at the ultraviolet fixed point. It turns out that the correct quantization for pure hole states is the one with half-integer quantum numbers originally proposed by Fioravanti et al. [Phys. Lett. B 390 (1997) 243]. Once the correct rule is imposed, the agreement between TCS and NLIE for pure hole states turns out to be impressive.     

Lagrangians for conformal gauge gravity and conformal simple supergravity

The connection, curvature, and Lagrangian for a conformal gauge gravity are obtained. A set of generators of the conformal simple supergroup is given, the commutation and anticommutation relations for the superalgebra are calculated, and a Lagrangian of the simple supergravity is established.     

W-geometry from chiral embeddings

Recent work by Y. Matsuo and the present author is summarized. It is shown that, classically, the conformal Toda equations associated with the simple lie algebras A_n sl (n + 1) follow from the embedding of particular 2D surfaces in CPⁿ. Since these Toda theories provide Noether realizations of W-symmetries, this gives the geometrical interpretation of the corresponding two-dimensional physics.     

Branching ratios for stopped pions in deuterium

The ratios $\text{S =}\text{ω(π}{}^{\mathrm{?}}\text{d}\text{→}\text{nn}\text{)}\text{ω(π}{}^{\mathrm{?}}\text{d}\text{→}\text{nn}\text{γ)}$ has been measured for negative pions stopping in deuterium gas at pressures up to 100 atm. The result is S = 2.83 ± 0.04 which is a factor of two more accurate than previous measurements.     

Slowdown for Time Inhomogeneous Branching Brownian Motion

We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but rather proportional to T ^1/3. We conjecture that this is the worse case correction possible.     

Projective embeddings of complex supermanifolds

We generalize the Kodaira Embedding Theorem and Chow's Theorem to the context of families of complex supermanifolds. In particular, we show that every family of super Riemann surfaces is a family of projective superalgebraic varieties.Research supported in part by NSF grant DMS-8704401Research supported in part by NSF grant DMS-4253943Research also supported in part by NSF grant DMS-4253943     

Haldane limits via Lagrangian embeddings

In the present paper we revisit the so-called Haldane limit, i.e. a particular continuum limit, which leads from a spin chain to a sigma model. We use the coherent state formulation of the path integral to reduce the problem to a semiclassical one, which leads us to the observation that the Haldane limit is closely related to a Lagrangian embedding into the classical phase space of the spin chain. Using this property, we find a spin chain whose limit produces a relativistic sigma model with target space the manifold of complete flags U(3)/U³(1). We discuss possible other future applications of Lagrangian/isotropic embeddings in this context.     

Spherical conformal models for compact stars

We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints.     

Off-shell conformal methods for the superstring

Superconformal field theory is used to compute off-shell amplitudes for the superstring. Off-shell three- and four-point functions in Witten's superstring field theory are obtained. The problem of gauge invariance due to the associativity anomaly in the bosonic sector is resolved to order g².