scholarly journals Emergent Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Robert de Mello Koch ◽  
Jia-Hui Huang ◽  
Minkyoo Kim ◽  
Hendrik J.R. Van Zyl
Keyword(s):  
Lattice Model ◽  
Quenched Disorder ◽  
Schur Polynomials ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
World Volume ◽  
Planar Limit ◽  
Integrable Spin ◽  
Mixing Problem ◽  
Giant Graviton

Abstract We study the spectrum of anomalous dimensions of operators dual to giant graviton branes. The operators considered belong to the su(2|3) sector of $$ \mathcal{N} $$ N = 4 super Yang-Mills theory, have a bare dimension ∼ N and are a linear combination of restricted Schur polynomials with p ∼ O(1) long rows or columns. In the same way that the operator mixing problem in the planar limit can be mapped to an integrable spin chain, we find that our problems maps to particles hopping on a lattice. The detailed form of the model is in precise agreement with the expected world volume dynamics of p giant graviton branes, which is a U(p) Yang-Mills theory. The lattice model we find has a number of noteworthy features. It is a lattice model with all-to-all sites interactions and quenched disorder.

scholarly journals One-loop non-planar anomalous dimensions in super Yang-Mills theory

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Tristan McLoughlin ◽  
Raul Pereira ◽  
Anne Spiering
Keyword(s):  
Perturbation Theory ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Mechanical Perturbation ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Scalar Products

Abstract We consider non-planar one-loop anomalous dimensions in maximally supersymmetric Yang-Mills theory and its marginally deformed analogues. Using the basis of Bethe states, we compute matrix elements of the dilatation operator and find compact expressions in terms of off-shell scalar products and hexagon-like functions. We then use non-degenerate quantum-mechanical perturbation theory to compute the leading 1/N2 corrections to operator dimensions and as an example compute the large R-charge limit for two-excitation states through subleading order in the R-charge. Finally, we numerically study the distribution of level spacings for these theories and show that they transition from the Poisson distribution for integrable systems at infinite N to the GOE Wigner-Dyson distribution for quantum chaotic systems at finite N.

Beta functions in Chirally deformed supersymmetric sigma models in two dimensions

2016 ◽  
Vol 31 (28n29) ◽  
pp. 1645040
Author(s):  
Arkady Vainshtein
Keyword(s):  
Sigma Models ◽  
Two Dimensions ◽  
Two Dimensional ◽  
World Sheet ◽  
Yang Mills ◽  
Anomalous Dimensions ◽  
Straightforward Method ◽  
The World ◽  
Original Formula

We study two-dimensional sigma models where the chiral deformation diminished the original [Formula: see text] supersymmetry to the chiral one, [Formula: see text]. Such heterotic models were discovered previously on the world sheet of non-Abelian stringy solitons supported by certain four-dimensional [Formula: see text] theories. We study geometric aspects and holomorphic properties of these models, and derive a number of exact expressions for the [Formula: see text] functions in terms of the anomalous dimensions analogous to the NSVZ [Formula: see text] function in four-dimensional Yang-Mills. Instanton calculus provides a straightforward method for the derivation.

scholarly journals A FOUR-FERMION LATTICE MODEL

1995 ◽  
Vol 10 (32) ◽  
pp. 4651-4669
Author(s):  
S. RANDJBAR-DAEMI ◽  
J. STRATHDEE
Keyword(s):  
Lattice Model ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Type Model ◽  
Dirac Fermions ◽  
Fermion Propagator ◽  
Yang Mills ◽  
Self Consistent ◽  
Low Energies ◽  
Local Symmetries

The weak coupling limit of an Ising type model on the F4 lattice is examined. It is shown that by imposing some constraints on the Ising couplings, one can express the weak coupling limit as a multidimensional Berezin integral with local symmetries, We explore the possibility of deriving a fermion propagator by a self-consistent, Nambu-Jona-Lasinio type of calculation. We argue that at low energies this model describes Dirac fermions coupled to Yang-Mills fields.

scholarly journals Fine structure of anomalous dimensions inN=4super-Yang–Mills theory

2009 ◽  
Vol 809 (1-2) ◽  
pp. 244-278 ◽  
Author(s):  
A.V. Belitsky ◽  
G.P. Korchemsky ◽  
R.S. Pasechnik
Keyword(s):  
Fine Structure ◽  
Yang Mills ◽  
Anomalous Dimensions

scholarly journals Exact Spectrum of Anomalous Dimensions of Planar N = 4 Supersymmetric Yang–Mills Theory: TBA and excited states

2010 ◽  
Vol 91 (3) ◽  
pp. 265-287 ◽  
Author(s):  
Nikolay Gromov ◽  
Vladimir Kazakov ◽  
Andrii Kozak ◽  
Pedro Vieira
Keyword(s):  
Excited States ◽  
Yang Mills ◽  
Anomalous Dimensions

scholarly journals Holographic baryons and instanton crystals

2015 ◽  
Vol 29 (16) ◽  
pp. 1540052 ◽  
Author(s):  
Vadim Kaplunovsky ◽  
Dmitry Melnikov ◽  
Jacob Sonnenschein
Keyword(s):  
Gauge Fields ◽  
Leading Order ◽  
Abelian Gauge ◽  
Yang Mills ◽  
World Volume ◽  
Dense Nuclear Matter ◽  
The World ◽  
The One ◽  
Holographic Description ◽  
Matter Phase

In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-Abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang–Mills instantons, whose solutions can be constructed from the celebrated Atiyah–Drinfeld–Hitchin–Manin (ADHM) construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review, we summarize the known results on the construction and phases of crystals of the holographic baryons.

scholarly journals Exact Spectrum of Anomalous Dimensions of PlanarN=4Supersymmetric Yang-Mills Theory

2009 ◽  
Vol 103 (13) ◽  
Author(s):  
Nikolay Gromov ◽  
Vladimir Kazakov ◽  
Pedro Vieira
Keyword(s):  
Yang Mills ◽  
Anomalous Dimensions

scholarly journals NONPLANAR INTEGRABILITY: BEYOND THE SU(2) SECTOR

2011 ◽  
Vol 26 (26) ◽  
pp. 4553-4583 ◽  
Author(s):  
ROBERT DE MELLO KOCH ◽  
BADR AWAD ELSEID MOHAMMED ◽  
STEPHANIE SMITH
Keyword(s):  
Harmonic Oscillators ◽  
Projection Operators ◽  
Young Diagrams ◽  
Schur Polynomials ◽  
Recursion Relations ◽  
Anomalous Dimensions ◽  
Dilatation Operator ◽  
Analytic Expressions ◽  
The One ◽  
Kravchuk Polynomials

We compute the one-loop anomalous dimensions of restricted Schur polynomials with a classical dimension Δ~O(N). The operators that we consider are labeled by Young diagrams with two long columns or two long rows. Simple analytic expressions for the action of the dilatation operator are found. The projection operators needed to define the restricted Schur polynomials are constructed by translating the problem into a spin chain language, generalizing earlier results obtained in the SU(2) sector of the theory. The diagonalization of the dilatation operator reduces to solving five term recursion relations. The recursion relations can be solved exactly in terms of products of symmetric Kravchuk polynomials with Hahn polynomials. This proves that the dilatation operator reduces to a decoupled set of harmonic oscillators and therefore it is integrable, extending a similar conclusion reached for the SU(2) sector of the theory.

scholarly journals Far beyond the planar limit in strongly-coupled $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shai M. Chester ◽  
Silviu S. Pufu
Keyword(s):  
Free Energy ◽  
Mass Parameter ◽  
Gauge Coupling ◽  
Superstring Theory ◽  
Exact Relation ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Planar Limit ◽  
Tensor Multiplet

Abstract When the SU(N) $$ \mathcal{N} $$ N = 4 super-Yang-Mills (SYM) theory with complexified gauge coupling τ is placed on a round four-sphere and deformed by an $$ \mathcal{N} $$ N = 2-preserving mass parameter m, its free energy F (m, τ,$$ \overline{\tau} $$ τ ¯ ) can be computed exactly using supersymmetric localization. In this work, we derive a new exact relation between the fourth derivative $$ {\partial}_m^4F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ m 4 F m τ τ ¯ m = 0 of the sphere free energy and the integrated stress-tensor multiplet four-point function in the $$ \mathcal{N} $$ N = 4 SYM theory. We then apply this exact relation, along with various other constraints derived in previous work (coming from analytic bootstrap, the mixed derivative $$ {\partial}_{\tau }{\partial}_{\overline{\tau}}{\partial}_m^2F\left(m,\tau, \overline{\tau}\right)\left|{{}_m}_{=0}\right. $$ ∂ τ ∂ τ ¯ ∂ m 2 F m τ τ ¯ m = 0 , and type IIB superstring theory scattering amplitudes) to determine various perturbative terms in the large N and large ’t Hooft coupling λ expansion of the $$ \mathcal{N} $$ N = 4 SYM correlator at separated points. In particular, we determine the leading large-λ term in the $$ \mathcal{N} $$ N = 4 SYM correlation function at order 1/N8. This is three orders beyond the planar limit.

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