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Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states

Vladimir V. Bazhanov
(
- Australian Natl. U., Canberra (main) and
- Australian Natl. U., Canberra
)
,
Sergei L. Lukyanov
(
- Rutgers U., Piscataway and
- Landau ITP, Chernogolovka
)

Oct 16, 2013

69 pages

Published in:

JHEP 09 (2014) 147

Published: Sep 25, 2014

e-Print:

1310.4390 [hep-th]

DOI:

10.1007/JHEP09(2014)147

Report number:

RUNHETC-2013-18

View in:

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Abstract: (Springer)

We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections on the punctured Riemann sphere, similarly to Hitchin’s self-duality equations. The proposed correspondence between the classical and quantum integrable systems provides a powerful tool for deriving functional and integral equations which determine the full spectrum of local integrals of motion for massive QFT in a finite volume. Potential applications of our results to the problem of non-perturbative quantization of classically integrable non-linear sigma models are briefly discussed.

Note:

63 pages, 8 figures; v2:typos corrected

Field Theories in Lower Dimensions
Integrable Field Theories
Integrable Hierarchies
field theory: massive
quantization: nonperturbative
sigma model: nonlinear
integrability
sinh-Gordon equation
finite size
integral equations

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Figures(8)

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