New Integrable 4D Quantum Field Theories from Strongly Deformed Planar N=4 Supersymmetric Yang-Mills Theory.
TLDR
A family of new integrable quantum field theories in four dimensions is introduced by considering the γ-deformed N=4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling, and an explicit conjecture is provided for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.Abstract:
We introduce a family of new integrable quantum field theories in four dimensions by considering the $\ensuremath{\gamma}$-deformed $\mathcal{N}=4$ supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the `t Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of $\mathrm{AdS}/\mathrm{CFT}$ integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single ``wheel'' graph, whose bulk represents an integrable ``fishnet'' graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar $\mathcal{N}=4$ SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.read more
Citations
More filters
Journal ArticleDOI
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
TL;DR: Conformal field theories have been long known to describe the universal physics of scale invariant critical points as discussed by the authors, and they describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same time sit at the heart of our modern understanding of quantum field theory.
Journal ArticleDOI
Hexagonalization of correlation functions
Thiago Fleury,Shota Komatsu +1 more
TL;DR: In this paper, a nonperturbative framework is proposed to study general correlation functions of single-trace operators in 4 supersymmetric Yang-Mills theory at large N, where the decomposition is akin to a triangulation of a Riemann surface, and thus call it hexagonalization.
Journal ArticleDOI
Elliptic Double-Box Integrals: Massless Scattering Amplitudes beyond Polylogarithms.
Jacob L. Bourjaily,Andrew J. McLeod,Marcus Spradlin,Marcus Spradlin,Matt von Hippel,Matthias Wilhelm +5 more
TL;DR: An analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms is derived, expressed directly in terms of dual-conformally invariant cross ratios; from this, the desired form is easily obtained.
Journal ArticleDOI
Walking, Weak first-order transitions, and Complex CFTs
TL;DR: In this paper, the authors discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics, and show how observables of the walking theory are computable by perturbing the complex CFTs.
Journal ArticleDOI
Integrability of conformal fishnet theory
Nikolay Gromov,Vladimir Kazakov,Vladimir Kazakov,Gregory P. Korchemsky,Stefano Negro,Grigory Sizov +5 more
TL;DR: The integrability of fishnet-type Feynman graphs arising in planar four-dimensional chiral theory was studied in this article, where it was shown that the transfer matrix for building the fishnet graphs emerges from the R−matrix of non-compact conformal SU(2, 2) Heisenberg spin chain with spins belonging to the principal series representations of the four dimensional conformal group.
References
More filters
Journal ArticleDOI
Review of AdS/CFT Integrability: An Overview
Niklas Beisert,Changrim Ahn,Luis F. Alday,Zoltan Bajnok,James M. Drummond,James M. Drummond,Lisa Freyhult,Nikolay Gromov,Nikolay Gromov,Romuald A. Janik,Vladimir Kazakov,Vladimir Kazakov,Thomas Klose,Thomas Klose,Gregory P. Korchemsky,Charlotte Kristjansen,Marc Magro,Marc Magro,Tristan McLoughlin,Joseph A. Minahan,Rafael I. Nepomechie,Adam Rej,Radu Roiban,Sakura Schafer-Nameki,Sakura Schafer-Nameki,Christoph Sieg,Christoph Sieg,Matthias Staudacher,Matthias Staudacher,Alessandro Torrielli,Alessandro Torrielli,Arkady A. Tseytlin,Pedro Vieira,Dmytro Volin,Konstantinos Zoubos +34 more
TL;DR: In this article, the authors present an overview of the achievements and the status of integrability in the context of the AdS/CFT correspondence as of the year 2010.
Journal ArticleDOI
Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
TL;DR: In this paper, it was shown that manifolds of fixed points, which are generated by exactly marginal operators, are common in N = 1 supersymmetric gauge theory, and a unified and simple prescription for identifying these operators, using tools similar to those employed in two-dimensional N = 2 supersymmetry.
Journal ArticleDOI
Lax pair for strings in Lunin-Maldacena background
TL;DR: In this paper, a T-duality-shift-Tduality (TsT) transformation was used to obtain the β-deformed background for real β ≡ γ, and it was shown that solutions of string theory equations of motion in this background are in one-to-one correspondence with those in AdS5 × S5 with twisted boundary conditions imposed on the U(1) isometry fields.
Journal ArticleDOI
Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory: TBA and excited states
TL;DR: An infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT are derived and it is proved that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics.
Journal ArticleDOI
Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang-Mills Theory
TL;DR: In this paper, a set of functional equations defining the anomalous dimensions of arbitrary local single trace operators in planar supersymmetric Yang-Mills theory is presented in the form of a $Y$ system based on the integrability of the dual superstring model.
Related Papers (5)
Review of AdS/CFT Integrability: An Overview
Niklas Beisert,Changrim Ahn,Luis F. Alday,Zoltan Bajnok,James M. Drummond,James M. Drummond,Lisa Freyhult,Nikolay Gromov,Nikolay Gromov,Romuald A. Janik,Vladimir Kazakov,Vladimir Kazakov,Thomas Klose,Thomas Klose,Gregory P. Korchemsky,Charlotte Kristjansen,Marc Magro,Marc Magro,Tristan McLoughlin,Joseph A. Minahan,Rafael I. Nepomechie,Adam Rej,Radu Roiban,Sakura Schafer-Nameki,Sakura Schafer-Nameki,Christoph Sieg,Christoph Sieg,Matthias Staudacher,Matthias Staudacher,Alessandro Torrielli,Alessandro Torrielli,Arkady A. Tseytlin,Pedro Vieira,Dmytro Volin,Konstantinos Zoubos +34 more