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J. M. Evans

Publications and source records attributed to J. M. Evans.

14 recordsLinked to original sources
arXiv2005

Quantum, higher-spin, local charges in symmetric space sigma models

Potential anomalies are analysed for the local spin-3 and spin-4 classically conserved currents in any two-dimensional sigma model on a compact symmetric space $G/H$, with $G$ and $H$ classical groups. Quantum local conserved charges are shown to exist in exactly those models which also possess quantum non-local (Yangian) charges. The possibility of larger sets of quantum local charges is discussed and shown to be consistent with known S-matrix results and the behaviour of the corresponding Yangian representations.

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arXiv2005

Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces

Local higher-spin conserved currents are constructed in the supersymmetric sigma models with target manifolds symmetric spaces $G/H$. One class of currents is based on generators of the de Rham cohomology ring of $G/H$; a second class of currents are higher-spin generalizations of the (super)energy-momentum tensor. A comprehensive analysis of the invariant tensors required to construct these currents is given from two complimentary points of view, and sets of primitive currents are identified from which all others can be constructed as differential polynomials. The Poisson bracket algebra of the top component charges of the primitive currents is calculated. It is shown that one can choose the primitive currents so that the bosonic charges all Poisson-commute, while the fermionic charges obey an algebra which is a form of higher-spin generalization of supersymmetry. Brief comments are made on some implications for the quantized theories.

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arXiv2004

Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)

Non-local conserved charges in two-dimensional sigma models with target spaces $SO(2n)/SO(n){\times}SO(n)$ and $Sp(2n)/Sp(n){\times}Sp(n)$ are shown to survive quantization, unspoiled by anomalies; these theories are therefore integrable at the quantum level. Local, higher-spin, conserved charges are also shown to survive quantization in the $SO(2n)/SO(n){\times}SO(n)$ models.

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arXiv2000

Commuting charges and symmetric spaces

Every classical sigma-model with target space a compact symmetric space $G/H$ (with $G$ classical) is shown to possess infinitely many local, commuting, conserved charges which can be written in closed form. The spins of these charges run over a characteristic set of values, playing the role of exponents of $G/H$, and repeating modulo an integer $h$ which plays the role of a Coxeter number.

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arXiv2000

Conserved charges and supersymmetry in principal chiral and WZW models

Conserved and commuting charges are investigated in both bosonic and supersymmetric classical chiral models, with and without Wess-Zumino terms. In the bosonic theories, there are conserved currents based on symmetric invariant tensors of the underlying algebra, and the construction of infinitely many commuting charges, with spins equal to the exponents of the algebra modulo its Coxeter number, can be carried out irrespective of the coefficient of the Wess-Zumino term. In the supersymmetric models, a different pattern of conserved quantities emerges, based on antisymmetric invariant tensors. The current algebra is much more complicated than in the bosonic case, and it is analysed in some detail. Two families of commuting charges can be constructed, each with finitely many members whose spins are exactly the exponents of the algebra (with no repetition modulo the Coxeter number). The conserved quantities in the bosonic and supersymmetric theories are only indirectly related, except for the special case of the WZW model and its supersymmetric extension.

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arXiv2000

Local conserved charges in principal chiral models

Local conserved charges in principal chiral models in 1+1 dimensions are investigated. There is a classically conserved local charge for each totally symmetric invariant tensor of the underlying group. These local charges are shown to be in involution with the non-local Yangian charges. The Poisson bracket algebra of the local charges is then studied. For each classical algebra, an infinite set of local charges with spins equal to the exponents modulo the Coxeter number is constructed, and it is shown that these commute with one another. Brief comments are made on the evidence for, and implications of, survival of these charges in the quantum theory.

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arXiv1999

On the Classification of Real Forms of Non-Abelian Toda Theories and W-algebras

We consider conformal non-Abelian Toda theories obtained by hamiltonian reduction from Wess-Zumino-Witten models based on general real Lie groups. We study in detail the possible choices of reality conditions which can be imposed on the WZW or Toda fields and prove correspondences with sl(2,R) embeddings into real Lie algebras and with the possible real forms of the associated W-algebras. We devise a a method for finding all real embeddings which can be obtained from a given embedding of sl(2,C) into a complex Lie algebra. We then apply this to give a complete classification of real embeddings which are principal in some simple regular subalgebra of a classical Lie algebra.

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arXiv1999

Conserved Charges and Supersymmetry in Principal Chiral Models

We report on investigations of local (and non-local) charges in bosonic and supersymmetric principal chiral models in 1+1 dimensions. In the bosonic PCM there is a classically conserved local charge for each symmetric invariant tensor of the underlying group. These all commute with the non-local Yangian charges. The algebra of the local charges amongst themselves is rather more subtle. We give a universal formula for infinite sets of mutually commuting local charges with spins equal to the exponents of the underlying classical algebra modulo its Coxeter number. Many of these results extend to the supersymmetric PCM, but with local conserved charges associated with antisymmetric invariants in the Lie algebra. We comment briefly on the quantum conservation of local charges in both the bosonic and super PCMs.

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arXiv1998

The No-ghost Theorem and Strings on AdS_3

A brief review of string theory on group manifolds is given, and comparisons are then drawn between Minkowski space, SU(2), and SU(1,1) = AdS_3. The proof of the no-ghost theorem is outlined, assuming a certain restriction on the representation content for bosonic and fermionic strings on SU(1,1). Some possible connections with the AdS/CFT correspondence are mentioned. (Based on invited talk by JME at Trieste Conference on Super 5-branes and Physics in (5+1)-dimensions.)

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arXiv1998

The No-ghost Theorem for AdS_3 and the Stringy Exclusion Principle

A complete proof of the No-ghost Theorem for bosonic and fermionic string theories on AdS_3, or the group manifold of SU(1,1), is given. It is then shown that the restriction on the spin (in terms of the level) that is necessary to obtain a ghost-free spectrum corresponds to the stringy exclusion principle of Maldacena and Strominger.

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arXiv1997

The Octonionic Membrane

We generalize the supermembrane solution of D=11 supergravity by permitting the 4-form $G$ to be either self-dual or anti-self-dual in the eight dimensions transverse to the membrane. After analyzing the supergravity field equations directly, and also discussing necessary conditions for unbroken supersymmetry, we focus on two specific, related solutions. The self-dual solution is not asymptotically flat. The anti-self-dual solution is asymptotically flat, has finite mass per unit area and saturates the same mass=charge Bogomolnyi bound as the usual supermembrane. Nevertheless, neither solution preserves any supersymmetry. Both solutions involve the octonionic structure constants but, perhaps surprisingly, they are unrelated to the octonionic instanton 2-form $F$, for which $TrF \wedge F$ is neither self-dual nor anti-self-dual.

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arXiv1996

Integrability vs. Supersymmetry

We investigate (1,0)-superconformal Toda theories based on simple Lie algebras and find that the classical integrability properties of the underlying bosonic theories do not survive. For several models based on algebras of low rank, we show explicitly that none of the conserved W-algebra generators can be generalized to the supersymmetric case. Using these results we deduce that at least one W-algebra generator fails to generalize in any model based on a classical Lie algebra. This argument involves a method for relating the bosonic Toda theories and their conserved currents within each classical series. We also scrutinize claims that the (1,0)-superconformal models actually admit (1,1) supersymmetry and find that they do not. Our results are consistent with the belief that all integrable Toda models with fermions arise from Lie superalgebras.

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arXiv1996

Real Forms of Non-abelian Toda Theories and their W-algebras

We consider real forms of Lie algebras and embeddings of sl(2) which are consistent with the construction of integrable models via Hamiltonian reduction. In other words: we examine possible non-standard reality conditions for non-abelian Toda theories. We point out in particular that the usual restriction to the maximally non-compact form of the algebra is unnecessary, and we show how relaxing this condition can lead to new real forms of the resulting W-algebras. Previous results for abelian Toda theories are recovered as special cases. The construction can be extended straightforwardly to deal with osp(1|2) embeddings in Lie superalgebras. Two examples are worked out in detail, one based on a bosonic Lie algebra, the other based on a Lie superalgebra leading to an action which realizes the N=4 superconformal algebra.

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