scholarly journals Local BCJ numerators for ten-dimensional SYM at one loop

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Elliot Bridges ◽  
Carlos R. Mafra
Keyword(s):  
Field Theory ◽  
Previous Analysis ◽  
Tree Level ◽  
Yang Mills ◽  
Analogous Manner ◽  
Different Color ◽  
Genus One ◽  
Super Yang Mills Theory

Abstract We obtain local numerators satisfying the BCJ color-kinematics duality at one loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for six points via the field-theory limit of the genus-one open superstring correlators for different color orderings, in an analogous manner to an earlier derivation of local BCJ-satisfying numerators at tree level from disk correlators. These results solve an outstanding puzzle from a previous analysis where the six-point numerators did not satisfy the color-kinematics duality.

scholarly journals Free BMN correlators with more stringy modes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Bao-ning Du ◽  
Min-xin Huang
Keyword(s):  
Transverse Direction ◽  
Point Function ◽  
Probability Interpretation ◽  
Yang Mills ◽  
Factorization Formula ◽  
Higher Genus ◽  
Pp Wave ◽  
String Diagram ◽  
Genus One ◽  
Super Yang Mills Theory

Abstract In the type IIB maximally supersymmetric pp-wave background, stringy excited modes are described by BMN (Berenstein-Madalcena-Nastase) operators in the dual $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. In this paper, we continue the studies of higher genus free BMN correlators with more stringy modes, mostly focusing on the case of genus one and four stringy modes in different transverse directions. Surprisingly, we find that the non-negativity of torus two-point functions, which is a consequence of a previously proposed probability interpretation and has been verified in the cases with two and three stringy modes, is no longer true for the case of four or more stringy modes. Nevertheless, the factorization formula, which is also a proposed holographic dictionary relating the torus two-point function to a string diagram calculation, is still valid. We also check the correspondence of planar three-point functions with Green-Schwarz string vertex with many string modes. We discuss some issues in the case of multiple stringy modes in the same transverse direction. Our calculations provide some new perspectives on pp-wave holography.

scholarly journals UNITARITY RELATIONS IN c=1 LIOUVILLE THEORY

1992 ◽  
Vol 07 (28) ◽  
pp. 2647-2657 ◽  
Author(s):  
DAVID A. LOWE
Keyword(s):  
Field Theory ◽  
Cosmological Constant ◽  
Particle Creation ◽  
Liouville Theory ◽  
Tree Level ◽  
S Matrix ◽  
The Matrix ◽  
Higher Genus ◽  
Genus One ◽  
Branch Cuts

We consider the S-matrix of c=1 Liouville theory with vanishing cosmological constant. We examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the "plus" tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, we show that the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. We conclude with some comments about the genus one (N,2) amplitudes.

scholarly journals Gravity loop integrands from the ultraviolet

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Alex Edison ◽  
Enrico Herrmann ◽  
Julio Parra-Martinez ◽  
Jaroslav Trnka
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Space ◽  
Indirect Evidence ◽  
Tree Level ◽  
Large Momentum ◽  
Recursion Relations ◽  
Yang Mills ◽  
The One ◽  
Geometric Picture ◽  
Super Yang Mills Theory

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.

scholarly journals SL(3, ℤ) Modularity and New Cardy limits of the $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Black Hole ◽  
Parameter Family ◽  
Similar Form ◽  
Four Dimensions ◽  
Yang Mills ◽  
Superconformal Index ◽  
Super Yang Mills Theory

Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

scholarly journals The Grassmannian for celestial superamplitudes

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Livia Ferro ◽  
Robert Moerman
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Minkowski Spacetime ◽  
Tree Level ◽  
Two Dimensional ◽  
Yang Mills ◽  
Celestial Sphere ◽  
Geometric Picture ◽  
Super Yang Mills Theory ◽  
The Way

Abstract Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.

scholarly journals Expansions of tree amplitudes for Einstein–Maxwell and other theories

2020 ◽  
Vol 2020 (7) ◽  
Author(s):  
Kang Zhou ◽  
Shi-Qian Hu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scattering Amplitudes ◽  
Recent Work ◽  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Quantum Field ◽  
Yang Mills

Abstract The expansions of tree-level scattering amplitudes for one theory into amplitudes for another theory, which have been studied in recent work, exhibit hidden connections between different theories that are invisible in the traditional Lagrangian formulism of quantum field theory. In this paper, the general expansion of tree Einstein–Maxwell amplitudes into the Kleiss–Kuijf basis of tree Yang–Mills amplitudes has been derived by applying a method based on differential operators. The obtained coefficients are shared by the expansion of tree $\phi^4$ amplitudes into tree BS (bi-adjoint scalar) amplitudes and the expansion of tree special Yang–Mills scalar amplitudes into tree BS amplitudes, as well the expansion of tree Dirac–Born–Infeld amplitudes into tree non-linear sigma model amplitudes.

scholarly journals Rotating restricted Schur polynomials

2017 ◽  
Vol 32 (25) ◽  
pp. 1750150 ◽  
Author(s):  
Nicholas Bornman ◽  
Robert de Mello Koch ◽  
Laila Tribelhorn
Keyword(s):  
Field Theory ◽  
Symmetry Algebra ◽  
Structural Features ◽  
Schur Polynomials ◽  
Small Perturbations ◽  
Yang Mills ◽  
Dilatation Operator ◽  
The One ◽  
Symmetry Generators ◽  
Super Yang Mills Theory

Large [Formula: see text] but nonplanar limits of [Formula: see text] super-Yang–Mills theory can be described using restricted Schur polynomials. Previous investigations demonstrate that the action of the one loop dilatation operator on restricted Schur operators, with classical dimension of order [Formula: see text] and belonging to the [Formula: see text] sector, is largely determined by the [Formula: see text] [Formula: see text] symmetry algebra as well as structural features of perturbative field theory. Studies presented so far have used the form of [Formula: see text] symmetry generators when acting on small perturbations of half-BPS operators. In this paper as a first step towards going beyond small perturbations of the half-BPS operators, we explain how the exact action of symmetry generators on restricted Schur polynomials can be determined.

scholarly journals Towards Feynman rules for conformal blocks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sarah Hoback ◽  
Sarthak Parikh
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Hypergeometric Functions ◽  
Power Series Expansion ◽  
Effective Field ◽  
Conformal Block ◽  
Tree Level ◽  
Conformal Blocks ◽  
Simple Set ◽  
Feynman Rules

Abstract We conjecture a simple set of “Feynman rules” for constructing n-point global conformal blocks in any channel in d spacetime dimensions, for external and exchanged scalar operators for arbitrary n and d. The vertex factors are given in terms of Lauricella hypergeometric functions of one, two or three variables, and the Feynman rules furnish an explicit power-series expansion in powers of cross-ratios. These rules are conjectured based on previously known results in the literature, which include four-, five- and six-point examples as well as the n-point comb channel blocks. We prove these rules for all previously known cases, as well as two new ones: the seven-point block in a new topology, and all even-point blocks in the “OPE channel.” The proof relies on holographic methods, notably the Feynman rules for Mellin amplitudes of tree-level AdS diagrams in a scalar effective field theory, and is easily applicable to any particular choice of a conformal block beyond those considered in this paper.

scholarly journals Super Yang-Mills theories with inhomogeneous mass deformations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yoonbai Kim ◽  
O-Kab Kwon ◽  
D. D. Tolla
Keyword(s):  
Boundary Condition ◽  
Killing Spinor ◽  
Vacuum Equation ◽  
Constant Mass ◽  
Yang Mills ◽  
Spatial Coordinate ◽  
Mass Functions ◽  
Vacuum Solutions ◽  
Super Yang Mills Theory

Abstract We construct the 4-dimensional $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 and $$ \mathcal{N} $$ N = 1 inhomogeneously mass-deformed super Yang-Mills theories from the $$ \mathcal{N} $$ N = 1* and $$ \mathcal{N} $$ N = 2* theories, respectively, and analyse their supersymmetric vacua. The inhomogeneity is attributed to the dependence of background fluxes in the type IIB supergravity on a single spatial coordinate. This gives rise to inhomogeneous mass functions in the $$ \mathcal{N} $$ N = 4 super Yang-Mills theory which describes the dynamics of D3-branes. The Killing spinor equations for those inhomogeneous theories lead to the supersymmetric vacuum equation and a boundary condition. We investigate two types of solutions in the $$ \mathcal{N}=\frac{1}{2} $$ N = 1 2 theory, corresponding to the cases of asymptotically constant mass functions and periodic mass functions. For the former case, the boundary condition gives a relation between the parameters of two possibly distinct vacua at the asymptotic boundaries. Brane interpretations for corresponding vacuum solutions in type IIB supergravity are also discussed. For the latter case, we obtain explicit forms of the periodic vacuum solutions.

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.

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