Enlarging local symmetries: A nonlocal Galilean model

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040009
Author(s):  
Luca Buoninfante ◽  
Gaetano Lambiase ◽  
Masahide Yamaguchi
Keyword(s):  
Infinite Order ◽  
Field Theories ◽  
Tree Level ◽  
Complex Conjugate ◽  
Nonlocal Operators ◽  
Graviton Propagator ◽  
Pole Structure ◽  
Local Symmetries ◽  
Spacetime Metric ◽  
Infinite Derivative

We consider the possibility to enlarge the class of symmetries realized in standard local field theories by introducing infinite order derivative operators in the actions, which become nonlocal. In particular, we focus on the Galilean shift symmetry and its generalization in nonlocal (infinite derivative) field theories. First, we construct a nonlocal Galilean model which may be UV finite, showing how the ultraviolet behavior of loop integrals can be ameliorated. We also discuss the pole structure of the propagator which has infinitely many complex conjugate poles, but satisfies tree level unitarity. Moreover, we will introduce the same kind of nonlocal operators in the context of linearized gravity. In such a scenario, the graviton propagator turns out to be ghost-free and the spacetime metric generated by a point-like source is non-singular.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

scholarly journals LECTURE NOTES ON INTERACTING QUANTUM FIELDS IN DE SITTER SPACE

2014 ◽  
Vol 23 (01) ◽  
pp. 1430001 ◽  
Author(s):  
E. T. AKHMEDOV
Keyword(s):  
De Sitter Space ◽  
The Self ◽  
Field Theories ◽  
Tree Level ◽  
Main Concern ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quantum Fields ◽  
De Sitter ◽  
Invariant States

We discuss peculiarities of quantum fields in de Sitter (dS) space on the example of the self-interacting massive real scalar, minimally coupled to the gravity background. Nonconformal quantum field theories (QFTs) in dS space show very special infrared behavior, which is not shared by quantum fields neither in flat nor in anti-dS space: in dS space loops are not suppressed in comparison with tree level contributions because there are strong infrared corrections. That is true even for massive fields. Our main concern is the interrelation between these infrared effects, the invariance of the QFT under the dS isometry and the (in)stability of dS invariant states (and of dS space itself) under nonsymmetric perturbations.

scholarly journals DIMENSION OF THE MODULI SPACE AND HAMILTONIAN ANALYSIS OF BF FIELD THEORIES

2011 ◽  
Vol 26 (18) ◽  
pp. 3013-3034 ◽  
Author(s):  
R. CARTAS-FUENTEVILLA ◽  
A. ESCALANTE-HERNANDEZ ◽  
J. BERRA-MONTIEL
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Canonical Analysis ◽  
Field Theories ◽  
Gauge Groups ◽  
Bf Theory ◽  
Extended Action ◽  
Local Symmetries ◽  
Hamiltonian Analysis

By using the Atiyah–Singer theorem through some similarities with the instanton and the antiinstanton moduli spaces, the dimension of the moduli space for two- and four-dimensional BF theories valued in different background manifolds and gauge groups scenarios is determined. Additionally, we develop Dirac's canonical analysis for a four-dimensional modified BF theory, which reproduces the topological YM theory. This framework will allow us to understand the local symmetries, the constraints, the extended Hamiltonian and the extended action of the theory.

Two Subfactors Arising from a Non-Degenerate Commuting Square II — Tensor Categories and TQFT's —

1997 ◽  
Vol 08 (03) ◽  
pp. 407-420 ◽  
Author(s):  
Nobuya Sato
Keyword(s):  
Field Theories ◽  
Complex Conjugate ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Tensor Categories ◽  
3 Dimensional ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

We prove that two subfactors N ⊂ M and P ⊂ Q arising from a non-degenerate commuting square have 3-dimensional topological quantum field theories (based on triangulations) complex conjugate to each other. Applying the asymptotic inclusion construction to each subfactor, we have new subfactors M ∨ (M′ ∩ M∞) ⊂ M∞ and Q ∨ (Q′ ∩ Q∞) ⊂ Q∞, then we also prove that the tensor categories of the M∞-M∞ bimodules and the Q∞-Q∞ bimodules are isomorphic to each other, if the two fusion graphs are connected. These results are based on our previous work and give a finer answer to a question raised by V. F. R. Jones in June, 1995.

scholarly journals Pole-skipping of scalar and vector fields in hyperbolic space: conformal blocks and holography

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Yongjun Ahn ◽  
Viktor Jahnke ◽  
Hyun-Sik Jeong ◽  
Keun-Young Kim ◽  
Kyung-Sun Lee ◽  
...  
Keyword(s):  
Hyperbolic Space ◽  
Vector Fields ◽  
Field Theories ◽  
Late Time ◽  
Time Behavior ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Scalar And Vector Fields ◽  
Pole Structure

Abstract Motivated by the recent connection between pole-skipping phenomena of two point functions and four point out-of-time-order correlators (OTOCs), we study the pole structure of thermal two-point functions in d-dimensional conformal field theories (CFTs) in hyperbolic space. We derive the pole-skipping points of two-point functions of scalar and vector fields by three methods (one field theoretic and two holographic methods) and confirm that they agree. We show that the leading pole-skipping point of two point functions is related with the late time behavior of conformal blocks and shadow conformal blocks in four-point OTOCs.

scholarly journals Cosmological Cutting Rules

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Scott Melville ◽  
Enrico Pajer
Keyword(s):  
Effective Field Theory ◽  
Effective Field ◽  
Field Theories ◽  
Tree Level ◽  
Optical Theorem ◽  
Loop Order ◽  
Founding Principle ◽  
Lower Loop ◽  
Infinite Set ◽  
The Universe

Abstract Primordial perturbations in our universe are believed to have a quantum origin, and can be described by the wavefunction of the universe (or equivalently, cosmological correlators). It follows that these observables must carry the imprint of the founding principle of quantum mechanics: unitary time evolution. Indeed, it was recently discovered that unitarity implies an infinite set of relations among tree-level wavefunction coefficients, dubbed the Cosmological Optical Theorem. Here, we show that unitarity leads to a systematic set of “Cosmological Cutting Rules” which constrain wavefunction coefficients for any number of fields and to any loop order. These rules fix the discontinuity of an n-loop diagram in terms of lower-loop diagrams and the discontinuity of tree-level diagrams in terms of tree-level diagrams with fewer external fields. Our results apply with remarkable generality, namely for arbitrary interactions of fields of any mass and any spin with a Bunch-Davies vacuum around a very general class of FLRW spacetimes. As an application, we show how one-loop corrections in the Effective Field Theory of inflation are fixed by tree-level calculations and discuss related perturbative unitarity bounds. These findings greatly extend the potential of using unitarity to bootstrap cosmological observables and to restrict the space of consistent effective field theories on curved spacetimes.

Effective Field Theories for Heavy Quarks: Heavy Quark Effective Theory and Heavy Quark Expansion

2020 ◽  
pp. 560-615
Author(s):  
Thomas Mannel
Keyword(s):  
Heavy Quark ◽  
Particle Physics ◽  
Operator Product Expansion ◽  
Effective Field ◽  
Field Theories ◽  
Effective Theory ◽  
Tree Level ◽  
Operator Product ◽  
Heavy Quark Effective Theory ◽  
Inclusive Decays

The heavy quark effective theory (HQET) and the heavy quark expansion (HQE) have developed into the standard tools in heavy-flavour physics. The lectures in this chapter introduce the basics of the approach and illustrates the methods by discussing some of their phenomenological applications. The chapter covers construction of the HQET Lagrangian, symmetries of HQET, HQET at one loop, and HQET applications to phenomenology. It also discusses HQE inclusive decays, operator product expansion (OPE), tree-level results, HQE parameters, QCD corrections, and end-point regions. It concludes by reiterating the enormous impact that both HQET and the HQE have had on particle physics phenomenology.

scholarly journals Transmutation of nonlocal scale in infinite derivative field theories

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
Luca Buoninfante ◽  
Anish Ghoshal ◽  
Gaetano Lambiase ◽  
Anupam Mazumdar
Keyword(s):  
Field Theories ◽  
Infinite Derivative

scholarly journals Tree-level S-matrix of superstring field theory with homotopy algebra structure

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Hiroshi Kunitomo
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Heterotic String ◽  
Field Theories ◽  
Tree Level ◽  
Algebra Structure ◽  
Type Ii ◽  
S Matrix ◽  
Homotopy Algebra

Abstract We show that the tree-level S-matrices of the superstring field theories based on the homotopy-algebra structure agree with those obtained in the first-quantized formulation. The proof is given in detail for the heterotic string field theory. The extensions to the type II and open superstring field theories are straightforward.

scholarly journals Two-photon processes in conformal QCD: resummation of the descendants of leading-twist operators

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
V.M. Braun ◽  
Yao Ji ◽  
A.N. Manashov
Keyword(s):  
Deeply Virtual Compton Scattering ◽  
Virtual Compton Scattering ◽  
Field Theories ◽  
Tree Level ◽  
Operator Product ◽  
Conformal Field Theories ◽  
Closed Expression ◽  
Conformal Field ◽  
Two Photon ◽  
Twist Operators

Abstract Using some techniques of conformal field theories, we find a closed expression for the contribution of leading twist operators and their descendants, obtained by adding total derivatives, to the operator product expansion (OPE) of two electromagnetic currents in QCD. Our expression resums contributions of all twists and to all orders in perturbation theory up to corrections proportional to the QCD β-function. At tree level and to twist-four accuracy, our result agrees with the expression derived earlier by a different method. The results are directly applicable to deeply-virtual Compton scattering and, e.g., γγ∗ annihilation in two mesons. As a byproduct, we derive a simple representation for the OPE of two scalar currents that is convenient for applications.

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