Quantization of sine-Gordon solitons on the circle: Semiclassical vs. exact results

Pawellek, Michael

doi:10.1016/j.nuclphysb.2008.10.001

Cited by 9 publications

(5 citation statements)

References 29 publications

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“…(C. 20) for (C.16). In various special cases the spectra and determinants of these operators have been studied in much detail, [38,39,40]. Therefore, it should be possible to compute the corresponding one-loop correction to the logarithm of the partition function at least numerically.…”

Section: C2 Some Other Examplesmentioning

confidence: 99%

Pohlmeyer-reduced form of string theory in AdS₅×S⁵: semiclassical expansion

Hoare¹,

Iwashita²,

Tseytlin³

2009

J. Phys. A: Math. Theor.

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We consider the Pohlmeyer-reduced formulation of the AdS5 ×S 5 superstring. It is constructed by introducing new variables which are algebraically related to supercoset current components so that the Virasoro conditions are automatically solved. The reduced theory is a gauged WZW model supplemented with an integrable potential and fermionic terms that ensure its UV finiteness. The original superstring theory and its reduced counterpart are closely related at the classical level, and we conjecture that they remain related at the quantum level as well, in the sense that their quantum partition functions evaluated on respective classical solutions are equal. We provide evidence for the validity of this conjecture at the one-loop level, i.e. at the first non-trivial order of the semiclassical expansion near several classes of classical solutions. 1 benjamin.hoare08@imperial.ac.uk 2 yukinori.iwashita07@imperial.ac.uk 3 Also at Lebedev Institute, Moscow. tseytlin@imperial.ac.uk P SU(2, 2 | 4) Sp(2, 2)×Sp(4) supercoset, which may be written in terms of the P SU (2, 2 | 4) current one may solve the Virasoro conditions by introducing the new variables g ∈ G = Sp(2, 2) × Sp(4), A ± ∈ h, 1 and Ψ L,R , which are algebraically related to the current components. The resulting equations can then be obtained from a local action I red (g, A ± , Ψ L,R ) which happens to be the G/H gauged WZW model modified by an H-invariant potential and supplemented by the 2-d fermionic terms (see [1] and (2.24),(2.25) below). This action, which defines the reduced theory, is 2-d Lorentz invariant and (after fixing the residual H gauge symmetry) involves only the physical number (8+8) of bosonic and fermionic degrees of freedom.The original AdS 5 × S 5 superstring theory and the reduced theory are essentially equivalent at the classical level, having closely related integrable structures and sets of classical solutions. The question that we would like to address here is if this correspondence may extend to the quantum level.Since the classical Pohlmeyer reduction utilizes conformal invariance, it has a chance to apply at the quantum level only if the sigma model one starts with is UV finite. This is the case for the AdS 5 × S 5 superstring sigma model, [19,20,21,22], which is a combination of the AdS 5 and the S 5 sigma models "glued" together by the Green-Schwarz fermions into a conformal 2-d theory. For consistency, the corresponding reduced theory, [1,2], should also be UV finite. That was indeed shown to be true to the two loop orders and is expected to be true also to all orders, [4].It should be emphasized that we are interested in the reduced theory only as a tool for describing observables of the original string theory: it is the string theory that should dictate those quantities one should compute in the reduced theory. 2We start with the 2-d worldsheet sigma model arising from the Green-Schwarz action for the Type IIB superstring theory on AdS 5 × S 5 after fixing the conformal gauge. This is the F/G coset sigma model where F = P SU (2,...

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Section: C2 Some Other Examplesmentioning

confidence: 99%

Pohlmeyer-reduced form of string theory in AdS₅×S⁵: semiclassical expansion

Hoare¹,

Iwashita²,

Tseytlin³

2009

J. Phys. A: Math. Theor.

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“…Although there were many different approaches to regularisation and semiclassical quantisation scheme, there was little progress in applying the method to nonlinear fields other then static kinks in infinite space. In recent years Pawellek has obtained energy corrections to a static, periodic solution of Sine-Gordon system in 1+1 dimensions [16] through a method developed by Kirsten and Loya [17] and a few years later energy corrections for static, periodic solutions of both Sine-Gordon and φ 4 systems embedded in a multidimensional theory were obtained as a power series in elliptic parameter around the single kink limit case [18].…”

Section: Introductionmentioning

confidence: 99%

Domain shape dependence of semiclassical corrections to energy

Kwiatkowski¹

2017

J. Phys. A: Math. Theor.

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“…Generalization for the supersymmetric kink is given in [13]. Solutions for Sine-Gordon quasiperiodic potentials was given in [14].…”

Section: Introductionmentioning

confidence: 99%

Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

Kwiatkowski

Leble

2013

Open Physics

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Abstract:The Heisenberg spin chain is considered in φ 4 model approximation. Quantum corrections to classical solutions of the one-dimensional φ 4 model within the correspondent physics are evaluated with account of rest −1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in a quasiclassical approximation. The results are applied to appropriate conditions of the spin chain model and its dynamics, for which elementary solutions, energy and the quantum corrections are calculated.PACS (

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Quantization of sine-Gordon solitons on the circle: Semiclassical vs. exact results

Cited by 9 publications

References 29 publications

Pohlmeyer-reduced form of string theory in AdS₅×S⁵: semiclassical expansion

Pohlmeyer-reduced form of string theory in AdS₅×S⁵: semiclassical expansion

Domain shape dependence of semiclassical corrections to energy

Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

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Quantization of sine-Gordon solitons on the circle: Semiclassical vs. exact results

Cited by 9 publications

References 29 publications

Pohlmeyer-reduced form of string theory in AdS5×S5: semiclassical expansion

Pohlmeyer-reduced form of string theory in AdS5×S5: semiclassical expansion

Domain shape dependence of semiclassical corrections to energy

Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

Contact Info

Product

Resources

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Pohlmeyer-reduced form of string theory in AdS₅×S⁵: semiclassical expansion

Pohlmeyer-reduced form of string theory in AdS₅×S⁵: semiclassical expansion