scholarly journals Strong coupling expansion of circular Wilson loops and string theories in AdS5 × S5 and AdS4 × CP3

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Simone Giombi ◽  
Arkady A. Tseytlin
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Strong Coupling ◽  
Strong Coupling Expansion ◽  
Open String ◽  
String Tension ◽  
Natural Generalization ◽  
Wilson Loops ◽  
Coupling Constant ◽  
Higher Genus

Abstract We revisit the problem of matching the strong coupling expansion of the $$ \frac{1}{2} $$ 1 2 BPS circular Wilson loops in $$ \mathcal{N} $$ N = 4 SYM and ABJM gauge theories with their string theory duals in AdS5× S5 and AdS4× CP3, at the first subleading (one-loop) order of the expansion around the minimal surface. We observe that, including the overall factor 1/gs of the inverse string coupling constant, as appropriate for the open string partition function with disk topology, and a universal prefactor proportional to the square root of the string tension T, both the SYM and ABJM results precisely match the string theory prediction. We provide an explanation of the origin of the $$ \sqrt{T} $$ T prefactor based on special features of the combination of one-loop determinants appearing in the string partition function. The latter also implies a natural generalization Zχ ∼ ($$ \sqrt{T}/{g}_{\mathrm{s}} $$ T / g s )χ to higher genus contributions with the Euler number χ, which is consistent with the structure of the 1/N corrections found on the gauge theory side.

scholarly journals WILSON LOOPS IN OPEN STRING THEORY

1988 ◽  
Vol 03 (03) ◽  
pp. 283-287 ◽  
Author(s):  
KIYOSHI SHIRAISHI
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Symmetry Breaking ◽  
Path Integral ◽  
Wilson Loop ◽  
Mass Spectra ◽  
Open String ◽  
Wilson Loops ◽  
Open Strings ◽  
Correct Weight

Wilson loop elements on torus are introduced into the partition function of open strings as Polyakov’s path integral at one-loop level. Mass spectra from compactification and expected symmetry breaking are illustrated by choosing the correct weight for the contributions from annulus and Möbius strip. We show that Jacobi’s imaginary transformation connects the mass spectra with the Wilson loops. The application to thermopartition function and cosmological implications are briefly discussed.

scholarly journals On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Beccaria ◽  
A. A. Tseytlin
Keyword(s):  
Strong Coupling ◽  
Wilson Loop ◽  
Root Function ◽  
String Tension ◽  
Wilson Loops ◽  
Square Root ◽  
Abjm Theory ◽  
Hooft Coupling ◽  
Higher Genus ◽  
Coupling Terms

Abstract Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop $$ \mathcal{W} $$ W in $$ \mathcal{N} $$ N = 4 SYM theory we work out their 1/N expansions in the limit of large ’t Hooft coupling λ. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling $$ {g}_{\mathrm{s}}\sim {g}_{\mathrm{YM}}^2\sim \lambda /N $$ g s ∼ g YM 2 ∼ λ / N and string tension $$ T\sim \sqrt{\lambda } $$ T ∼ λ . Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of $$ \left\langle \mathcal{W}\right\rangle $$ W is a series in $$ {g}_{\mathrm{s}}^2/T $$ g s 2 / T , the correlator of the Wilson loop with chiral primary operators $$ {\mathcal{O}}_J $$ O J has expansion in powers of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ g s 2 / T 2 . Like in the case of $$ \left\langle \mathcal{W}\right\rangle $$ W where these leading terms are known to resum into an exponential of a “one-handle” contribution $$ \sim {g}_{\mathrm{s}}^2/T $$ ∼ g s 2 / T , the leading strong coupling terms in $$ \left\langle {\mathcal{WO}}_J\right\rangle $$ WO J sum up to a simple square root function of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ g s 2 / T 2 . Analogous expansions in powers of $$ {g}_{\mathrm{s}}^2/T $$ g s 2 / T are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.

scholarly journals Nonlocal Scalar Quantum Field Theory—Functional Integration, Basis Functions Representation and Strong Coupling Expansion

Particles ◽  
2019 ◽  
Vol 2 (3) ◽  
pp. 385-410 ◽  
Author(s):  
Matthew Bernard ◽  
Vladislav A. Guskov ◽  
Mikhail G. Ivanov ◽  
Alexey E. Kalugin ◽  
Stanislav L. Ogarkov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Strong Coupling ◽  
Functional Integration ◽  
Strong Coupling Expansion ◽  
Basis Functions ◽  
Model Parameters ◽  
Quantum Field ◽  
Primary Field ◽  
Coupling Constant

Nonlocal quantum field theory (QFT) of one-component scalar field φ in D-dimensional Euclidean spacetime is considered. The generating functional (GF) of complete Green functions Z as a functional of external source j, coupling constant g and spatial measure d μ is studied. An expression for GF Z in terms of the abstract integral over the primary field φ is given. An expression for GF Z in terms of integrals over the primary field and separable Hilbert space (HS) is obtained by means of a separable expansion of the free theory inverse propagator L ^ over the separable HS basis. The classification of functional integration measures D φ is formulated, according to which trivial and two nontrivial versions of GF Z are obtained. Nontrivial versions of GF Z are expressed in terms of 1-norm and 0-norm, respectively. In the 1-norm case in terms of the original symbol for the product integral, the definition for the functional integration measure D φ over the primary field is suggested. In the 0-norm case, the definition and the meaning of 0-norm are given in terms of the replica-functional Taylor series. The definition of the 0-norm generator Ψ is suggested. Simple cases of sharp and smooth generators are considered. An alternative derivation of GF Z in terms of 0-norm is also given. All these definitions allow to calculate corresponding functional integrals over φ in quadratures. Expressions for GF Z in terms of integrals over the separable HS, aka the basis functions representation, with new integrands are obtained. For polynomial theories φ 2 n , n = 2 , 3 , 4 , … , and for the nonpolynomial theory sinh 4 φ , integrals over the separable HS in terms of a power series over the inverse coupling constant 1 / g for both norms (1-norm and 0-norm) are calculated. Thus, the strong coupling expansion in all theories considered is given. “Phase transitions” and critical values of model parameters are found numerically. A generalization of the theory to the case of the uncountable integral over HS is formulated—GF Z for an arbitrary QFT and the strong coupling expansion for the theory φ 4 are derived. Finally a comparison of two GFs Z , one on the continuous lattice of functions and one obtained using the Parseval–Plancherel identity, is given.

scholarly journals Lattice study of area law for double-winding Wilson loops

2018 ◽  
Vol 175 ◽  
pp. 12010
Author(s):  
Akihiro Shibata ◽  
Seikou Kato ◽  
Kei-Ichi Kondo ◽  
Ryutaro Matsudo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Strong Coupling ◽  
Wilson Loop ◽  
Strong Coupling Expansion ◽  
Wilson Loops ◽  
Yang Mills ◽  
Lattice Monte Carlo ◽  
Area Law

We study the double-winding Wilson loops in the SU(N) Yang-Mills theory on the lattice. We discuss how the area law falloff of the double-winding Wilson loop average is modified by changing the enclosing contours C1 and C2 for various values of the number of color N. By using the strong coupling expansion, we evaluate the double-winding Wilson loop average in the lattice SU(N) Yang-Mills theory. Moreover, we compute the double-winding Wilson loop average by lattice Monte Carlo simulations for SU(2) and SU(3). We further discuss the results from the viewpoint of the Non-Abelian Stokes theorem in the higher representations.

scholarly journals The disk partition function in string theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Lorenz Eberhardt ◽  
Sridip Pal
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Open String ◽  
Infinite Volume ◽  
Conformal Gauge ◽  
Negative Volume

Abstract We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group PSL(2, ℝ) on the worldsheet even after fixing the conformal gauge. It naively has infinite volume and leads to a vanishing answer. We use different methods that all demonstrate that PSL(2, ℝ) effectively behaves like a group with finite negative volume in the path integral, which leads to a simple prescription for the computation of the disk partition function. We apply our findings to give a simple rederivation of the D-brane tensions.

scholarly journals Bell's Inequalities, Superquantum Correlations, and String Theory

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Lay Nam Chang ◽  
Zachary Lewis ◽  
Djordje Minic ◽  
Tatsu Takeuchi ◽  
Chia-Hsiung Tze
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
String Theory ◽  
String Tension ◽  
Coupling Constant ◽  
Bell’S Inequalities ◽  
Deformation Parameters ◽  
Usual Quantum ◽  
Bell's Inequalities

We offer an interpretation of superquantum correlations in terms of a “doubly” quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tensionα', and the string coupling constantgs, is such a superquantum theory that transgresses the usual quantum violations of Bell's inequalities. We also discuss theℏ→∞limit of quantum mechanics in this context. As a superquantum theory, string theory should display distinct experimentally observable supercorrelations of entangled stringy states.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

scholarly journals Drell-Yan Cross Section to Third Order in the Strong Coupling Constant

2020 ◽  
Vol 125 (17) ◽  
Author(s):  
Claude Duhr ◽  
Falko Dulat ◽  
Bernhard Mistlberger
Keyword(s):  
Strong Coupling ◽  
Cross Section ◽  
Strong Coupling Constant ◽  
Coupling Constant ◽  
Third Order
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