scholarly journals Nonperturbative study of the jet quenching parameter from AdS/CFT

2014 ◽  
Vol 29 ◽  
pp. 1460253
Author(s):  
De-Fu Hou ◽  
Zi-Qiang Zhang ◽  
Hai-Cang Ren
Keyword(s):  
Sigma Model ◽  
Theoretical Calculations ◽  
Strong Coupling Expansion ◽  
Jet Quenching ◽  
Nonzero Temperature ◽  
World Sheet ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Classical World ◽  
Leading Term

This talk presents our derivation of the jet quenching parameter of 𝒩 = 4 super symmetric Yang-Mills theory to the sub-leading term in the large 't Hooft coupling λ at a nonzero temperature by including the world-sheet fluctuations around the classical world sheet from AdS /CFT. The strong coupling expansion corresponds to the semi-classical expansion of the string-sigma model, the gravity dual of the Wilson loop operator, with the sub-leading term expressed in terms of functional determinants of fluctuations. The contribution of these determinants are evaluated numerically. We find the jet quenching parameter is reduced due to world sheet fluctuations by a factor (1 - 1.97λ-1/2). Some insights have been discussed by the comparison between experimental data and our result and other theoretical calculations.

K-VORTEX DYNAMICS IN $\mathcal{N}\, = \,1^*$ THEORY AND IN ITS GRAVITY DUAL

2010 ◽  
Vol 25 (02n03) ◽  
pp. 247-257
Author(s):  
R. AUZZI
Keyword(s):  
Magnetic Flux ◽  
Scaling Law ◽  
World Sheet ◽  
Flux Tubes ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Higgs Vacuum ◽  
Large N ◽  
Vortex Solutions ◽  
Magnetic Flux Tubes

We study magnetic flux tubes in the Higgs vacuum of the [Formula: see text] mass deformation of SU(Nc), [Formula: see text] SYM and its large Nc string dual, the Polchinski-Strassler geometry. Choosing equal masses for the three adjoint chiral multiplets, for all Nc we identify a "colour-flavour locked" symmetry, SO(3)C+F which leaves the Higgs vacuum invariant. At weak coupling, we find explicit non-Abelian k-vortex solutions carrying a ℤNc-valued magnetic flux, with topological winding 0 < k < Nc. These k-strings spontaneously break SO(3)C+F to U(1)C+F resulting in an S2 moduli space of solutions. The world-sheet sigma model is a nonsupersymmetric ℂℙ1 model with a theta angle θ1+1 = k(Nc - k)θ3+1 where θ3+1 is the Yang-Mills vacuum angle. We find numerically that k-vortex tensions follow the Casimir scaling law Tk ∝ k(Nc - k) for large Nc. In the large Nc IIB string dual, the SO(3)C+F symmetry is manifest in the geometry interpolating between AdS5 × S5 and the interior metric due to a single D5 -brane carrying D3 -brane charge. We identify candidate k-vortices as expanded probe D3 -branes formed from a collection of k D -strings. The resulting k-vortex tension exhibits precise Casimir scaling, and the effective world-sheet theta angle matches the semiclassical result. S -duality maps the Higgs to the confining phase so that confining string tensions at strong 't Hooft coupling also exhibit Casimir scaling in [Formula: see text] theory in the large Nc limit.

scholarly journals THE PARISI–SOURLAS MECHANISM IN YANG–MILLS THEORY?

2000 ◽  
Vol 15 (11) ◽  
pp. 1613-1628
Author(s):  
J. A. MAGPANTAY
Keyword(s):  
Random Field ◽  
Dimensional Reduction ◽  
Degrees Of Freedom ◽  
Sigma Model ◽  
Gauge Condition ◽  
Yang Mills ◽  
Equivalent Theory ◽  
Leading Term ◽  
Nonlinear Gauge

The Parisi–Sourlas mechanism is exhibited in pure Yang–Mills theory. Using the new scalar degrees of freedom derived from the nonlinear gauge condition, we show that the nonperturbative sector of Yang–Mills theory is equivalent to a 4D O(1, 3) sigma model in a random field. We then show that the leading term of this equivalent theory is invariant under supersymmetry transformations where [Formula: see text] is unchanged. This leads to dimensional reduction proving the equivalence of the nonperturbative sector of Yang–Mills theory to a 2D O(1, 3) sigma model.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals New bi-harmonic superspace formulation of 4D, $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
I. L. Buchbinder ◽  
E. A. Ivanov ◽  
V. A. Ivanovskiy
Keyword(s):  
Effective Action ◽  
Harmonic Superspace ◽  
Four Dimensions ◽  
Yang Mills ◽  
Convenient Tool ◽  
Leading Term

Abstract We develop a novel bi-harmonic $$ \mathcal{N} $$ N = 4 superspace formulation of the $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory (SYM) in four dimensions. In this approach, the $$ \mathcal{N} $$ N = 4 SYM superfield constraints are solved in terms of on-shell $$ \mathcal{N} $$ N = 2 harmonic superfields. Such an approach provides a convenient tool of constructing the manifestly $$ \mathcal{N} $$ N = 4 supersymmetric invariants and further rewriting them in $$ \mathcal{N} $$ N = 2 harmonic superspace. In particular, we present $$ \mathcal{N} $$ N = 4 superfield form of the leading term in the $$ \mathcal{N} $$ N = 4 SYM effective action which was known previously in $$ \mathcal{N} $$ N = 2 superspace formulation.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals THE PROPER TIME FORMALISM, GAUGE INVARIANCE AND THE EFFECTS OF A FINITE WORLD SHEET CUTOFF IN STRING THEORY

1995 ◽  
Vol 10 (31) ◽  
pp. 4501-4519 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Transformation ◽  
Gauge Invariance ◽  
Proper Time ◽  
World Sheet ◽  
Massive Mode ◽  
Yang Mills ◽  
Previous Discussion ◽  
Time Formalism ◽  
Klein Gordon ◽  
Type Interaction

We discuss the issue of going off-shell in the proper time formalism. This is done by keeping a finite world sheet cutoff. We construct one example of an off-shell covariant Klein-Gordon type interaction. For a suitable choice of the gauge transformation of the scalar field, gauge invariance is maintained off-mass-shell. However, at the second order in the gauge field interaction, one finds that [U(1)] gauge invariance is violated due to the finite cutoff. Interestingly, we find, to the lowest order, that by adding a massive mode with appropriate gauge transformation laws to the sigma model background, we can restore gauge invariance. The gauge transformation law is found to be consistent, to the order calculated, with what one expects from the interacting equation of motion of the massive field. We also extend some previous discussion on applying the proper time formalism for propagating gauge particles, to the interacting (i.e. Yang-Mills) case.

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

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