arXiv subjects

Jonas Bjornsson

Publications and source records attributed to Jonas Bjornsson.

11 recordsLinked to original sources

arXiv2010

Modular invariant partition functions for non-compact G/Ad(H) models

We propose a spectrum for a class of gauged non-compact G/Ad(H) WZNW models, including spectrally flowed images of highest, lowest, and mixed extremal weight modules. These are combined into blocks whose characters, due to the Lorentzian signature of the target space, are divergent and treated as formal expressions in need of regularisation. Assuming that this is possible, we show that these extended characters transform linearly under modular transformations, and can be used to write down modular invariant partition functions.

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arXiv2010

Multi-loop amplitudes in maximally supersymmetric pure spinor field theory

This paper provides a more detailed background to the results of arXiv:1004.2692 concerning properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised field theory version of the non-minimal pure spinor formalism originally designed for describing superstring amplitudes. In addition to superspace world-line fields, the formalism involves a set of world-line ghost fields that are required for implementing BRST invariance with a composite b ghost. In particular, we show that BRST invariance requires the presence of certain contact terms. For four-point amplitudes, these are important beyond two loops. We also present an alternative proof of the "no-triangle hypothesis" and the vanishing of amplitudes with fewer than four external particles.

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arXiv2010

5 loops in 24/5 dimensions

A first quantised approach to loop amplitudes based on the pure spinor particle is applied to the systematics of four-particle amplitudes in maximally supersymmetric field theories. Counting of fermionic zero modes allows the identification of momentum factors multiplying R**4 in the case of supergravity (and F**4 in the Yang--Mills case) thereby making manifest their ultraviolet properties as a function of dimension, D. For L=2,3,4 loops the leading supergravity divergence is in D=4+6/L dimensions and proportional to d*2L R**4, in line with earlier field theory calculations. However, at five loops there is a radical change in the systematics, suggesting the presence of a contribution with an explicit L=5 logarithmic ultraviolet divergence when D=24/5 that is proportional to d*8 R**4. We further argue that d*8 R**4 should receive contributions from all loops, which would imply that N=8 supergravity (with D=4) is not protected by supersymmetry from a seven-loop divergence.

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arXiv2010

WZNW Strings, Unitarity and Anti de Sitter spaces

We investigate the unitarity of strings on non-trivial space-time backgrounds based on gauged WZNW models involving SO(n,2), gauging an SO(n,1) subgroup. As geometric coset spaces, these are Anti de Sitter spaces. Our present models are more complicated than the ones considered previously, for example those connected to Hermitian symmetric spaces. In the present case, the time-like field component is not a center of the maximal compact subalgebra, leading to several additional complications. Assuming discrete representations, it will only be possible to consider n even, resulting in odd dimensional spaces. We will prove that such models are free of ghosts for a class of discrete representations.

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arXiv2010

Gauged non-compact WZNW models, revisited

The purpose of the present paper is to investigate the necessary conditions for unitarity of the spectrum of non-compact gauged WZNW models to some depth. In particular, we would like to investigate the necessity of integer weights and level. We will learn that the problem is very complex and we have not found any simple and general way to formulate the necessary conditions. Instead one must resort to studying the problem almost case by case. The only nearly complete conditions that we will find, is for the case g = su(n,1). Furthermore, the horizontal part of the case g = su(p,q) is nearly completed as well. In other cases, we will find conditions associated with certain subalgebras and nodes in the Dynkin diagram close to the one corresponding to the non-compact root. In these examples we can give conditions for the horizontal part of the algebra. As a by-product of our investigation we will prove some nice formulae of character identities and explicit branching functions for these representations.

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arXiv2009

On the unitarity of gauged non-compact world-sheet supersymmetric WZNW models

In this paper we generalize our investigation of the unitarity of non-compact WZNW models connected to Hermitian symmetric spaces to the N=1 world-sheet supersymmetric extension of these models. We will prove that these models have a unitary spectrum in a BRST approach for antidominant highest weight representations if the level and weights of the gauged subalgebra are integers. We will find new critical string theories in 7 and 9 space-time dimensions.

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arXiv2008

On the unitarity of gauged non-compact WZNW strings

In this paper we investigate the unitarity of gauged non-compact WZNW strings i.e. string theories formulated as G/H' WZNW models, where G is a non-compact group. These models represent string theories on non-trivial curved space-times with one time-like component. We will prove that for the class of models connected to Hermitian symmetric spaces, and a natural set of discrete highest weight representations, the BRST formulation, in which the gauging is defined through a BRST condition, yields unitarity. Unitarity requires the level times the Dynkin index to be an integer, as well as integer valued highest weights w.r.t. the compact subalgebra. We will also show that the BRST formulation is not equivalent to the conventional GKO coset formulation, defined by imposing a highest weight condition w.r.t. H'. The latter leads to non-unitary physical string states.This is, to our knowledge, the first example of a fundamental difference between the two formulations.

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arXiv2008

On small tension p-branes

This paper deals with p-branes with small but non-zero tension. We prove the existence of canonical transformations, within a perturbation theory, that link specific geometries of p-branes to solvable theories, namely string-like and particle-like theories. The specific shapes correspond to stretched configurations. For configurations linked to string-like theories one will upon quantization get a critical dimension of (25+p).

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arXiv2005

The BRST treatment of stretched membranes

The BRST-invariant formulation of the bosonic stretched membrane is considered. In this formulation the stretched membrane is given as a perturbation around zero-tension membranes, where the BRST-charge decomposes as a sum of a string-like BRST-charge and a perturbation. It is proven, by means of cohomology techniques, that there exists to any order in perturbation theory a canonical transformation that reduces the full BRST-charge to the string-like one. It is also shown that one may extend the results to the quantum level yielding a nilpotent charge in 27 dimensions.

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arXiv2005

Stretched quantum membranes

We study bosonic and space-time supersymmetric membranes with small tensions corresponding to stretched configurations. Using a generalized lightcone gauge, one may set up a perturbation theory around configurations having zero tension. We will show, by explicit construction to all orders in perturbation theory, that these membrane configurations are canonically equivalent, and thereby solvable, to string-like configurations with string excitations transverse to the stretched direction. At the quantum level, it is shown that there exists an ordering such that equivalence by unitary transformations is achieved. Consistency requires the critical dimensions 27 and 11 for the bosonic and supersymmetric cases, respectively. The mass spectrum is determined to any order. It is discrete and contains massless exitations. The ground state is purely string-like, whereas excited string-like states split through the perturbation into an infinite set of states with equal or lower energies.

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arXiv2004

The membrane as a perturbation around string-like configurations

The bosonic membrane in a partial gauge, where one space dimension is eliminated, is formulated as a perturbation theory around an exact free string-like solution. This perturbative regime corresponds to a situation where one of the world-volume space-like dimensions is much greater than the other, so that the membrane has the form of a narrow band or large hoop with string excitations being transverse to the widest dimension. The perturbative equations of motion are studied and solved to first order. Furthermore, it is shown for the open or semi-open cases and to any order in perturbation theory, that one may find canonical transformations that will transform the membrane Hamiltonian into a free string-like Hamiltonian and a boundary Hamiltonian. Thus the membrane dynamics in our perturbation scheme is essentially captured by an interacting boundary theory defined on a two-dimensional world-sheet. A possible implication of this to M-theory is discussed.

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