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to the scatterings of particles. The leading finite size effect of a multiparticle state comes from the quantization of momenta which is dictated by the scattering matrix. It incorporates all polynomial corrections in the inverse of the volume. In addition, there are exponentially small (Lüscher) corrections and their leading contributions come from the polarization of the sea of virtual particles. For small volumes, these effects become dominant and one needs to perform a resummation of the virtual corrections, which sometimes can be carried out in the form of nonlinear integral equations.
The analogous program for the form factors in finite volume is still in its infancy, although it follows essentially the same conceptual steps. The polynomial finite-size corrections in the inverse of the volume are taken into account by changing the normalization of states and restricting the momenta to satisfy the quantization condition. The exponentially small corrections and their possible resummation, however, have been only conjectured for diagonal form factors.
In the simplest holographic duality we are interested not only in the spectral problem of the corresponding integrable two dimensional QFT but we also would like to determine the finite volume form factors of certain defect creating operators.
String theory on the AdS₅×S⁵ background is integrable and its spectrum is conjectured to be in one-to-one correspondence with the anomalous dimensions of gauge-invariant operators in the maximally supersymmetric 4D gauge theory. In the implementation of the bootstrap program the spectral part is basically completed: the scattering matrix has been calculated and the model is solved in infinite volume. In finite volume the leading polynomial finite size corrections were described by the Beisert-Staudacher equations and the leading Lüscher correction of multiparticle states was developed by us and successfully applied for the simplest operators. We also managed to write a finite number of coupled nonlinear integral equations to describe the ground state and some excited-state energies. Recently a very elegant formulation of the finite volume spectral problem has been achieved by the so-called quantum spectral curve method. These are finite coupled equations, which relate the jump of the appearing functions to each other, and has been conjectured for certain special states and sectors of the theory.
Recently we extended the exact description of the spectrum for other sectors of the theory.
Specifically, we analyzed two very interesting physical problems: the exact description of the quark anti-quark potential and the tachyonic instability of the brane anti-brane system.
For the quark anti-quark potential we proposed a novel formulation in terms of a system of coupled integral equations, which allowed a systematic weak coupling expansion. We expanded our equations to next-to-leading order and tested the results against direct two-loop gauge theory computations. We found complete agreement.
We also developed a complete description of the brane anti-brane system both in terms of a gauge theory and an integrable model. This enabled us to study tachyons in string theory, which are non-perturbative objects signalling instabilities.
As the spectral problem is conceptually completed, we started to analyze the application of the form-factor bootstrap program to the holographic duality. During the investigation we
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observed that there are two kinematically complementary domains of the three-point functions of the conformal invariant maximally supersymmetric gauge theory.
In the first case one of the operators does not carry any charge on the sphere and the three-point function is related to a diagonal finite volume matrix element of a local operator. We started to develop a programme to calculate these matrix elements via diagonal finite volume form factors valid for any 't Hooft coupling neglecting vacuum polarization effects.
As a starting point, we investigated the strong coupling limit of these matrix elements which we mapped to classical form factors of the analogous and well-known sine-Gordon quantum field theory. We conjectured that the diagonal form factors of any local operator can be obtained by averaging the operator for the moduli space of classical solutions. We checked this conjecture thoroughly both in infinite and finite volumes.
In the other (and complementary) kinematical domain all the operators have some charge on the sphere. We found that the three point functions do not correspond to form factors of local operators on the world-sheet, rather they correspond to form factors of a defect/boundary-creating operator. In order to gain intuition and new techniques, we developed a form factor bootstrap for such operators in simple integrable toys models and calculated their leading finite-size effects.
Grants
OTKA K 81461: Two dimensional quantum field theories and their applications (Z. Bajnok 2010-2015)
OTKA K 83267: Relativistic particle systems (J. Balog 2011-2015)
OTKA K 109312: Holographic solution to measure theories (Á. Hegedűs 2013-2015)
HoloGrav ESF Network: Holographic methods for strongly coupled systems (Z. Bajnok 2012-2016)
“Momentum” Program of the HAS (Z. Bajnok 2012-2017)
International cooperation
MTA Hungarian-Japanese bilateral: Integrability in gauge gravity duality and strong coupling dynamics of gauge theory; Kyoto, Tokyo and Tsukuba (Z. Bajnok, 2013-2014)
TÉT French-Hungarian bilateral: Application of spin chains and super strings to study fundamental interactions: the integrability side of the AdS/CFT correspondence; Paris Saclay and ENS (J. Balog, 2013-2014)
MTA Hungarian-Polish bilateral: Gauge string duality and its applications; Krakow (Z. Bajnok 2013-2015)
Hungarian-Korean-Polish collaboration: On the Gauge-string duality, Seoul, Krakow (Z.
Bajnok 2013-2014)
Long term visitors
Ines Aniceto, Lisbon University-31 (Z. Bajnok, 2014.03.02)
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Publications
Articles
1. Aoki S, Balog J, Weisz P: Walking in the 3-dimensional large N scalar model. J HIGH ENERGY PHYS, 09: Paper 167. 27 p. (2014)
2. Bajnok Z, Balog J, Correa DH, Hegedus A, Schaposnik Massolo FI, Tóth GZ: Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion. J HIGH ENERGY PHYS, 2014:(3) Paper 056. 31 p. (2014)
3. Bajnok Z, Drukker N, Hegedus A, Nepomechie RI, Palla L, Sieg C, Suzuki R: The spectrum of tachyons in AdS/CFT. J HIGH ENERGY PHYS, 2014:(3) Paper 055. 47 p. (2014)
4. Bajnok Z, Buccheri F, Hollo L, Konczer J, Takacs G: Finite volume form factors in the presence of integrable defects. NUCL PHYS B, 882:(1) pp. 501-531. (2014)
5. Bajnok Z, Kim MY, Palla L: Spectral curve for open strings attached to the y = 0 brane. J HIGH ENERGY PHYS, 2014:(4) Paper 035. 33 p. (2014)
6. Bajnok Z, Holló L, Watts G: Defect scaling Lee-Yang model from the perturbed DCFT point of view. NUCL PHYS B, 886: pp. 93-124. (2014)
7. Bajnok Z, Janik RA, Wereszczynski A: HHL correlators, orbit averaging and form factors. J HIGH ENERGY PHYS, 09: Paper 050. 32 p. (2014)
8. Balog J: An exact solution of the Currie-Hill equations in 1 + 1 dimensional Minkowski space. PHYS LETT A, 378:(47) pp. 3488-3496. (2014)
9. Hollo L, Laczko ZB, Bajnok Z: Explicit boundary form factors: The scaling Lee-Yang model. NUCL PHYS B, 886: pp. 1029-1045. (2014)
10. Tóth GZs: Higher spin fields with reversed spin-statistics relation. INT J MOD PHYS A, 29: Paper 1450129. 34 p. (2014)
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