Boundary states in c=−2 logarithmic conformal field theory

Starting from first principles, a constructive method is presented to obtain boundary states in conformal field theory. It is demonstrated that this method is well suited to compute the boundary states of logarithmic conformal field theories. By studying the logarithmic conformal field theory with central charge c=−2 in detail, we show that our method leads to consistent results. In particular, it allows to define boundary states corresponding to both, indecomposable representations as well as their irreducible subrepresentations.     

Phenomenology and conformal field theory or can string theory predict the weak mixing angle?

We show that the weak mixing angle θ_w is the same for continuously connected classical vacua of the heterotic string which have chiral fermions in their massless spectra. We also show that the world-sheet quantum field theory for any classical vacuum with spacetime supersymmetry possesses an N = 2 superconformal invariance.     

The group of local biholomorphisms of ℂ1 and conformal field theory in the operator formalism

Motivated by the operator formulation of conformal field theory on Riemann surfaces, we study the properties of the infinite dimensional group of local biholomorphic transformations (conformal reparametrizations) of ¹ and develop elements of its representation theory.     

Derivation of the polyakov string theory from planar φ3 field theory

A rigorous derivation is given of the Polyakov surface theory by summing over all planar Feynman graphs of a φ³ scalar field theory. It uses a discretization of surfaces through the triangulation induced by the dual graphs of the Feynman graphs. No approximation is made for the propagators and the metric is shown to be locally defined. The Green's functions of both theories are shown to coincide for any finite external momenta.     

Warped string compactification via singular Calabi–Yau conformal field theory

We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2,R)$\mathit{SL}(2,\mathbf{R})$. The discrete spectrum is automatically consistent with the GSO projection in the continuous sector, and contains massless matter fields localized on a four-dimensional submanifold at the tip of a cigar. In particular, they are in the 27⊕1$27\oplus 1$ of E₆$E_6$ for the E₈×E₈$E_8\times E_8$ heterotic string. We speculate about a possible realization of local E₆$E_6$ GUT by using this framework.     

Flat coordinates of topological conformal field theory and solutions of the Gauss–Manin system

A luminescent trace has been observed in a ruby crystal (Al₂O₃: Cr³⁺) that rotates at a frequency of 2 to 200 Hz and is irradiated by 532-nm coherent electromagnetic radiation. A method has been proposed to determine the lifetime of the excited electronic state of chromium ions from the measurement of the length of an arc of the trajectory of a light spot on the surface of a rotating ruby single crystal. A “comet trace” formed at the passage of radiation through the rotating crystal near the absorption band of the material has been detected inside the ruby crystal. It has been shown that the theory based on the analysis of the motion of polaritons in the rotating reference frame is in satisfactory agreement with experimental results.     

The Sine-Gordon field theory model at α2=8π, the non-superrenormalizable theory

We study the Sine-Gordon field theory at ²=8. We prove that the theory is renormalizable but not superrenormalizable and we show how the perturbative renormalization procedure works in this case where the interaction is not polynomial. To go beyond the perturbative results we investigate the -functional equation for this theory and discuss in what sense at ²=8 the theory is lacking the asymptotic freedom and how it is asymptotic free for ²<8 in a appropriate region of the coupling constants.     

The role of conformal symmetry in the Jackiw–Pi model

The Jackiw–Pi model in 2+1$2+1$ dimensions is a non-relativistic conformal field theory of charged particles with point-like self-interaction. For specific values of the interaction strengths the classical theory possesses vortex and multi-vortex solutions, which are all degenerate in energy. We compute the full set of first-order perturbative quantum corrections. Only the coupling constant g²$g^2$ requires renormalization; the fields and electric charge e are not renormalized. It is shown that in general the conformal symmetries are broken by an anomalous contribution to the conservation law, proportional to the β-function. However, the β  -function vanishes upon restricting the coupling constants to values g²=±e²$g^2=\pm e^2$, which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.     

Existence of the critical point in φ4 field theory

We consider the ⁴ quantum field theory in two and three spacetime dimensions. In the single phase region the physical mass (inverse correlation length)m() decreases continuously to zero as the bare mass parameter approaches a critical value _c from above. In three dimensions the critical point _c is in the single phase region and the physical mass vanishes there,m( _c )=0.A consequence of our results is that the critical exponentv governing the approach to infinite correlations is bounded below (rigorously) by its classical value, 1/2.Supported in part by the National Science Foundation under Grant MPS74-13252     

Quantum field theory as effective BV theory from Chern–Simons

The general procedure for obtaining explicit expressions for all cohomologies of Berkovits' operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern–Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two-dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of “singular” point from the perspective of the suggested method for cohomology evaluation. For arbitrary “regular” point the same technique results in AKSZ (Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern–Simons theory (BF theory) in accord with [N. Berkovits, Covariant quantization of the superparticle using pure spinors, JHEP 0109 (2001) 016, hep-th/0105050; N. Berkovits, ICTP lectures on covariant quantization of the superstring, hep-th/0209059; M. Movshev, A. Schwarz, On maximally supersymmetric Yang–Mills theories, Nucl. Phys. B 681 (2004) 324, hep-th/0311132; M. Movshev, A. Schwarz, Algebraic structure of Yang–Mills theory, hep-th/0404183].     

Analytic and numerical evidence from quantum field theory for the hyperscaling relation dv = 2Δ−γ in the d=3 ising model

The hyperscaling relationdv = 2 - (d=3) for the Ising model has been shown to follow from a constructive approach proposed by one of the authors (R.S.) of a relativistic theory of self-interacting Bosons in d space-time dimensions. We present evidence that the two assumptions made in this approach are valid: On a finite Euclidean (hyper-) cubical lattice in d dimensions the renormalization map from the bare to the renormalized parameters should have nonvanishing Jacobian everywhere. We show this analytically and numerically on the boundary set of the parameters. The numerical analysis involves Monte Carlo calculations in the region where the bare coupling constantg ₀ is infinite, giving the Ising model. The linear sizen of the lattice (with periodic boundary conditions) was taken to be 5, 6, and 10. There we also checked the second assumption saying that the correlation length for the Ising model is a monotonic function of the temperature. We also comment on the possible numbers of zeros of the Callan-Symanzik function of this theory.     

Limiting transition from the model of collective motion of π-electrons in molecules to the semiempirical Pariser-Parr-Pople theory

In the context of a two-parameter scheme (correlation and localization) we examine the region of applicability of various-electron theories. The limiting transition from the model of collective motion (MCM) to Pariser-Parr-Pople (PPP) theory shows that PPP theory is inconsistent. The PPP model Hamiltonian derived in the approximation of strong localization of-electrons has been invalidly extended to the region of weak localization, thus losing an important branch of low-lying collective-electron excitations. Inclusion of this branch qualitatively alters the results of PPP theory. Furthermore, the conclusion of PPP theory that there are no singlet excitations of the benzene molecule below 4.7 eV conflicts with several experiments.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 37–42, September, 1977.