scholarly journals More on holographic correlators: twisted and dimensionally reduced structures

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Connor Behan ◽  
Pietro Ferrero ◽  
Xinan Zhou
Keyword(s):  
Field Theory ◽  
Theoretical Data ◽  
Infinite Family ◽  
Tree Level ◽  
Chiral Algebra ◽  
Perfect Agreement ◽  
Four Dimensions ◽  
Independent Field ◽  
Superconformal Theories ◽  
Emergent Structure

Abstract Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $$ \mathcal{N} $$ N = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

scholarly journals Correlation functions of spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Evgeny I. Buchbinder ◽  
Jessica Hutomo ◽  
Sergei M. Kuzenko
Keyword(s):  
Field Theory ◽  
Correlation Functions ◽  
Field Theories ◽  
Point Function ◽  
Superconformal Field Theories ◽  
Superconformal Symmetry ◽  
Four Dimensions ◽  
Superconformal Field Theory ◽  
Superconformal Theories ◽  
Spinor Current

Abstract We consider $$ \mathcal{N} $$ N = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet Sα and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with $$ \mathcal{N} $$ N = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume $$ \mathcal{N} $$ N = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the $$ \mathcal{N} $$ N = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the $$ \mathcal{N} $$ N = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in $$ \mathcal{N} $$ N = 1 superconformal field theory does not necessarily imply $$ \mathcal{N} $$ N = 2 superconformal symmetry.

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 Superconformal boundaries in 4 − ϵ dimensions

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Aleix Gimenez-Grau ◽  
Pedro Liendo ◽  
Philine van Vliet
Keyword(s):  
Three Dimensional ◽  
Spacetime Dimension ◽  
Perfect Agreement ◽  
Bootstrap Analysis ◽  
First Order ◽  
Free Theory ◽  
First Order Correction ◽  
Free Parameters ◽  
Superconformal Theories ◽  
Zumino Model

Abstract Boundaries in three-dimensional $$ \mathcal{N} $$ N = 2 superconformal theories may preserve one half of the original bulk supersymmetry. There are two possibilities which are characterized by the chirality of the leftover supercharges. Depending on the choice, the remaining 2d boundary algebra exhibits $$ \mathcal{N} $$ N = (0, 2) or $$ \mathcal{N} $$ N = (1) supersymmetry. In this work we focus on correlation functions of chiral fields for both types of supersymmetric boundaries. We study a host of correlators using superspace techniques and calculate superconformal blocks for two- and three-point functions. For $$ \mathcal{N} $$ N = (1) supersymmetry, some of our results can be analytically continued in the spacetime dimension while keeping the codimension fixed. This opens the door for a bootstrap analysis of the ϵ-expansion in supersymmetric BCFTs. Armed with our analytically-continued superblocks, we prove that in the free theory limit two-point functions of chiral (and antichiral) fields are unique. The first order correction, which already describes interactions, is universal up to two free parameters. As a check of our analysis, we study the Wess-Zumino model with a super-symmetric boundary using Feynman diagrams, and find perfect agreement between the perturbative and bootstrap results.

scholarly journals Topological excitations in statistical field theory at the upper critical dimension

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marco Panero ◽  
Antonio Smecca
Keyword(s):  
Field Theory ◽  
Monte Carlo Study ◽  
Critical Dimension ◽  
Density Profiles ◽  
Upper Critical Dimension ◽  
Four Dimensions ◽  
Topological Excitations ◽  
Classical Heisenberg Model ◽  
Statistical Field ◽  
Statistical Field Theory

Abstract We present a high-precision Monte Carlo study of the classical Heisenberg model in four dimensions. We investigate the properties of monopole-like topological excitations that are enforced in the broken-symmetry phase by imposing suitable boundary conditions. We show that the corresponding magnetization and energy-density profiles are accurately predicted by previous analytical calculations derived in quantum field theory, while the scaling of the low-energy parameters of this description questions an interpretation in terms of particle excitations. We discuss the relevance of these findings and their possible experimental applications in condensed-matter physics.

scholarly journals Evaluating EYM amplitudes in four dimensions by refined graphic expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hongxiang Tian ◽  
Enze Gong ◽  
Chongsi Xie ◽  
Yi-Jian Du
Keyword(s):  
Tree Level ◽  
Tree Amplitude ◽  
Four Dimensions ◽  
Yang Mills ◽  
Negative Helicity ◽  
Spanning Forests ◽  
Single Trace

Abstract The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − or $$ \left({h}_i^{-},{g}_j^{-}\right) $$ h i − g j − configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

scholarly journals Chiral correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Flat Space ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Four Dimensions ◽  
Yang Mills ◽  
The Matrix ◽  
Superspace Formalism ◽  
Model Approach

Abstract We consider a family of $$ \mathcal{N} $$ N = 2 superconformal field theories in four dimensions, defined as ℤq orbifolds of $$ \mathcal{N} $$ N = 4 Super Yang-Mills theory. We compute the chiral/anti-chiral correlation functions at a perturbative level, using both the matrix model approach arising from supersymmetric localisation on the four-sphere and explicit field theory calculations on the flat space using the $$ \mathcal{N} $$ N = 1 superspace formalism. We implement a highly efficient algorithm to produce a large number of results for finite values of N , exploiting the symmetries of the quiver to reduce the complexity of the mixing between the operators. Finally the interplay with the field theory calculations allows to isolate special observables which deviate from $$ \mathcal{N} $$ N = 4 only at high orders in perturbation theory.

TREE DIAGRAMS IN WITTEN’S SUPERSTRING FIELD THEORY

1989 ◽  
Vol 04 (21) ◽  
pp. 2063-2071
Author(s):  
GEORGE SIOPSIS
Keyword(s):  
Field Theory ◽  
Scattering Amplitudes ◽  
Invariant Theory ◽  
Higher Order ◽  
Contact Term ◽  
Tree Level ◽  
Gauge Invariant

It is shown that the contact term discovered by Wendt is sufficient to ensure finiteness of all tree-level scattering amplitudes in Witten’s field theory of open superstrings. Its inclusion in the action also leads to a gauge-invariant theory. Thus, no additional higher-order counterterms in the action are needed.

scholarly journals Cosmological phase transitions: is effective field theory just a toy?

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Marieke Postma ◽  
Graham White
Keyword(s):  
Field Theory ◽  
Phase Transition ◽  
Phase Transitions ◽  
Effective Field Theory ◽  
New Physics ◽  
Effective Field ◽  
Tree Level ◽  
Dark Sector ◽  
First Order ◽  
First Order Phase

Abstract To obtain a first order phase transition requires large new physics corrections to the Standard Model (SM) Higgs potential. This implies that the scale of new physics is relatively low, raising the question whether an effective field theory (EFT) description can be used to analyse the phase transition in a (nearly) model-independent way. We show analytically and numerically that first order phase transitions in perturbative extensions of the SM cannot be described by the SM-EFT. The exception are Higgs-singlet extension with tree-level matching; but even in this case the SM-EFT can only capture part of the full parameter space, and if truncated at dim-6 operators, the description is at most qualitative. We also comment on the applicability of EFT techniques to dark sector phase transitions.

scholarly journals EFFECTIVE AVERAGE ACTION IN STATISTICAL PHYSICS AND QUANTUM FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 1951-1982 ◽  
Author(s):  
CHRISTOF WETTERICH
Keyword(s):  
Field Theory ◽  
Statistical Physics ◽  
Thermal Fluctuations ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Quantum Field ◽  
Four Dimensions ◽  
Average Action ◽  
Exact Renormalization Group ◽  
Unified Description

An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We present a simple unified description of critical phenomena for O(N)-symmetric scalar models in two, three or four dimensions, including essential scaling for the Kosterlitz-Thouless transition.

Degenerate classical minima and instantons

2021 ◽  
pp. 942-959
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Ground State ◽  
Stochastic Dynamics ◽  
Minimum Energy ◽  
Two Dimensions ◽  
Quantum Theories ◽  
Four Dimensions ◽  
Quantum Tunnelling ◽  
Charge Conjugation Parity ◽  
Double Well Potential

Instantons play an important role in the following situation: quantum theories corresponding to classical actions that have non-continuously connected degenerate minima. The simplest examples are provided by one-dimensional quantum systems with symmetries and potentials with non-symmetric minima. Classically, the states of minimum energy correspond to a particle sitting at any of the minima of the potential. The position of the particle breaks (spontaneously) the symmetry of the system. By contrast, in quantum mechanics (QM), the modulus of the ground-state wave function is large near all the minima of the potential, as a consequence of barrier penetration effects. Two typical examples illustrate this phenomenon: the double-well potential, and the cosine potential, whose periodic structure is closer to field theory examples. In the context of stochastic dynamics, instantons are related to Arrhenius law. The proof of the existence of instantons relies on an inequality related to supersymmetric structures, and which generalizes to some field theory examples. Again, the presence of instantons again indicates that the classical minima are connected by quantum tunnelling, and that the symmetry between them is not spontaneously broken. Examples of such a situation are provided, in two dimensions, by the charge conjugation parity (CP) (N − 1) models and, in four dimensions, by SU(2) gauge theories.

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