Semi-classical spectrum of the homogeneous sine-Gordon theories

Fernández-Pousa, Carlos R.; Miramontes, J. Luis

doi:10.1016/s0550-3213(98)00060-1

Cited by 38 publications

(52 citation statements)

References 63 publications

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“…This point of view motivated the construction of a whole set of new factorizable scattering matrices with colour values in [3] by extending S-matrices proposed earlier [4] in the context of the so-called simply-laced Homogeneous Sine-Gordon (HSG) models [5] to a much larger class. In the present work the construction scheme outlined in [3] will be generalized to involve also non simply-laced Lie algebras for the colour values by choosing the semi-classical particle spectrum [6] of the so-called non simply-laced HSG models as input data for the bootstrap (3). The resulting factorizable S-matrices might be interpreted as possible candidates for these integrable quantum field theories.…”

Section: Introductionmentioning

confidence: 99%

Colours associated to nonsimply-laced Lie algebras and exact S-matrices

Korff

2001

Physics Letters B

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A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non simply-laced Lie algebras. This in particular leads to a coupling of different affine Toda models whose fusing structure has to be matched in a suitable manner. The definition of the new S-matrices is motivated by the semi-classical particle spectrum of the non simply-laced Homogeneous Sine-Gordon (HSG) models, which are integrable perturbations of WZNW cosets. In particular, the S-matrices of the simply-laced HSG models are recovered as a special case.

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Section: Introductionmentioning

confidence: 99%

Colours associated to nonsimply-laced Lie algebras and exact S-matrices

Korff

2001

Physics Letters B

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“…The origin of the topological charge is both the existence of different vacua and the fact that G 0 can be non simply connected. This is in contrast with the solitons of the HSG theories which are not topological but carry a U (1) rg abelian Noether charge [12]. In general, the solitons of a generic SSSG theory corresponding to a perturbation of a coset CFT of the form G/H are expected to carry both topological charges and abelian Noether charges related to a global symmetry of the classical action specified by H. In this sense, they are analogous to the dyons in four-dimensional nonabelian gauge theories [21].…”

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confidence: 79%

“…Nevertheless, for a generic SSSG theory p = 0 and the solitons will carry both topological and U(1) p Noether charges, which make them similar to the dyons in four-dimensional non-abelian gauge theories [21] Taking into account that the sine-Gordon theory is the Split model corresponding to SU(2)/SO(2), a number of explicit soliton solutions for the Split models can be obtained by embedding the sine-Gordon solitons in the regular SU(2) subgroups of G. This method is widely used in the context of Yang-Mills theories based on arbitrary Lie groups to construct monopole or instanton solutions by embeddings of the SU(2) spherically symmetric 't-Hooft-Polyakov monopole [31] or the self-dual SU(2) BelavinPolyakov-Schwartz-Tyupkin instanton [32]. It has also been used to construct the soliton solutions of the affine Toda theories with imaginary coupling constant [33] and, more recently, to construct the soliton solutions of the HSG theories starting with the Complex sine-Gordon solitons [12]. For each positive root α of G, let us consider the field configuration h = exp(φt α / √ α 2 ), which trivially satisfies the constraints in (2.6).…”

Section: Soliton Solutionsmentioning

confidence: 99%

“…In general, the solitons of a generic SSSG theory corresponding to a perturbation of a coset CFT of the form G/H are expected to carry both topological charges and abelian Noether charges related to a global symmetry of the classical action specified by H. In this sense, they are analogous to the dyons in four-dimensional nonabelian gauge theories [21]. Another relevant feature of the solitons of the Split models, which is expected to be shared with other SSSG theories, is that their mass spectrum suggests that some of them might describe unstable particles in the quantum theory, which is analogous to what happens in the HSG theories [12,13]. Actually, the unstability of the heaviest solitons in the spectrum has been checked by Brazhnikov in the SSSG theories related to SU(3)/SO(3).…”

mentioning

confidence: 93%

“…This theory corresponds to the perturbation of the usual Z k -parafermions by the first thermal operator [8], whose exact factorizable scattering matrix is the minimal one associated to a k−1 [9,10]. The quantum integrability of the HSG theories for arbitrary G was established in [11], its soliton spectrum was obtained in [12], and a proposal for the exact factorizable S-matrices of the theories related to simply laced Lie groups G has been made in [13]. The main feature of those S-matrices is that they possess resonance poles which can be associated directly to the presence of unstable particles in the spectrum via the classical Lagrangian.…”

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confidence: 99%

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Massive symmetric space sine-Gordon soliton theories and perturbed conformal field theory

Alvaredo

Miramontes

2000

Nuclear Physics B

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The perturbed conformal field theories corresponding to the massive Symmetric Space sine-Gordon soliton theories are identified by calculating the central charge of the unperturbed conformal field theory and the conformal dimension of the perturbation. They are described by an action with a positive-definite kinetic term and a real potential term bounded from below, their equations of motion are non-abelian affine Toda equations and, moreover, they exhibit a mass gap. The unperturbed CFT corresponding to the compact symmetric space G/G 0 is either the WZNW action for G 0 or the gauged WZNW action for a coset of the form G 0 /U (1) p . The quantum integrability of the theories that describe perturbations of a WZNW action, named Split models, is established by showing that they have quantum conserved quantities of spin +3 and −3. Together with the already known results for the other massive theories associated with the non-abelian affine Toda equations, the Homogeneous sine-Gordon theories, this supports the conjecture that all the massive Symmetric Space sine-Gordon theories will be quantum integrable and, hence, will admit a factorizable S-matrix. The general features of the soliton spectrum are discussed, and some explicit soliton solutions for the Split models are constructed. In general, the solitons will carry both topological charges and abelian Noether charges. Moreover, the spectrum is expected to include stable and unstable particles.

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Tree-level S-matrix of Pohlmeyer reduced form of AdS 5 × S 5 superstring theory

Hoare

Tseytlin

2010

J. High Energ. Phys.

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With a motivation to find a 2-d Lorentz-invariant solution of the AdS 5 × S 5 superstring we continue the study of the Pohlmeyer-reduced form of this theory. The reduced theory is constructed from currents of the superstring sigma model and is classically equivalent to it. Its action is that of G/H = Sp(2, 2) × Sp(4)/[SU (2)] 4 gauged WZW model deformed by an integrable potential and coupled to fermions. This theory is UV finite and is conjectured to be related to the superstring theory also at the quantum level. Expanded near the trivial vacuum it has the same elementary excitations (8+8 massive bosonic and fermionic 2-d degrees of freedom) as the AdS 5 × S 5 superstring in the S 5 light-cone gauge or near plane-wave expansion. In contrast to the superstring case, the interaction terms in the reduced action are manifestly 2-d Lorentz invariant. Since the theory is integrable, its S-matrix should be effectively determined by the two-particle scattering. Here we explicitly compute the tree-level two-particle S-matrix for the elementary excitations of the reduced theory. We find that this S-matrix has the same index structure and group factorization properties as the superstring S-matrix computed in hep-th/0611169 but has simpler coefficients, depending only on the difference of two rapidities. While the gauge-fixed form of the reduced action has only the bosonic [SU (2)] 4 part of the P SU (2|2) × P SU (2|2) symmetry of the light-cone superstring spectrum as its manifest symmetry we conjecture that it should also have a hidden fermionic symmetry that effectively interchanges bosons and fermions and which should guide us towards understanding the relation between the two S-matrices.

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Semi-classical spectrum of the homogeneous sine-Gordon theories

Cited by 38 publications

References 63 publications

Colours associated to nonsimply-laced Lie algebras and exact S-matrices

Colours associated to nonsimply-laced Lie algebras and exact S-matrices

Massive symmetric space sine-Gordon soliton theories and perturbed conformal field theory

Tree-level S-matrix of Pohlmeyer reduced form of AdS 5 × S 5 superstring theory

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