scholarly journals Effective field theory for closed strings near the Hagedorn temperature

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ram Brustein ◽  
Yoav Zigdon
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Conformal Structure ◽  
Effective Field ◽  
Conformally Invariant ◽  
Conformal Field ◽  
Quartic Interaction

Abstract We discuss interacting, closed, bosonic and superstrings in thermal equilibrium at temperatures close to the Hagedorn temperature in flat space. We calculate S-matrix elements of the strings at the Hagedorn temperature and use them to construct a low-energy effective action for interacting strings near the Hagedorn temperature. We show, in particular, that the four-point amplitude of massless winding modes leads to a positive quartic interaction. Furthermore, the effective field theory has a generalized conformal structure, namely, it is conformally invariant when the temperature is assigned an appropriate scaling dimension. Then, we show that the equations of motion resulting from the effective action possess a winding-mode-condensate background solution above the Hagedorn temperature and present a worldsheet conformal field theory, similar to a Sine-Gordon theory, that corresponds to this solution. We find that the Hagedorn phase transition in our setup is second order, in contrast to a first-order transition that was found previously in different setups.

scholarly journals An explicit construction of the dimension-9 operator basis in the standard model effective field theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Equations Of Motion ◽  
Baryon Number ◽  
Explicit Construction ◽  
Effective Field ◽  
Starting Point ◽  
The Standard Model ◽  
Symmetry Relations

Abstract We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ 384 Δ B = 0 Δ L = ± 2 + 10 Δ B = ± 2 Δ L = 0 + 4 Δ B = ± 1 Δ L = ± 3 + 236 Δ B = ± 1 Δ L = ∓ 1 operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ 44874 Δ B = 0 Δ L = ± 2 + 2862 Δ B = ± 2 Δ L = 0 + 486 Δ B = ± 1 Δ L = ± 3 + 42234 Δ B = ∓ 1 Δ L = ± 1 operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.

scholarly journals On the one-loop calculations with Reggeized quarks

2017 ◽  
Vol 32 (40) ◽  
pp. 1750207 ◽  
Author(s):  
Maxim Nefedov ◽  
Vladimir Saleev
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Field Theory ◽  
Effective Action ◽  
Gauge Invariance ◽  
Effective Field ◽  
Loop Correction ◽  
Gauge Invariant ◽  
The One ◽  
Regge Limit

The technique of one-loop calculations for the processes involving Reggeized quarks is described in the framework of gauge invariant effective field theory for the Multi-Regge limit of QCD, which has been introduced by Lipatov and Vyazovsky. The rapidity divergences, associated with the terms enhanced by log(s), appear in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and [Formula: see text]-scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop [Formula: see text] amplitude. The cancellation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.

CONSISTENCY BETWEEN THE S-MATRIX AND THE SIGMA- MODEL APPROACHES TO THE CLOSED STRING EFFECTIVE ACTION ON THE DISC

1988 ◽  
Vol 03 (06) ◽  
pp. 561-569 ◽  
Author(s):  
L.V. ROZHANSKY ◽  
A.A. TSEYTLIN
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Action ◽  
Sigma Model ◽  
Closed String ◽  
Effective Field ◽  
Cosmological Term ◽  
S Matrix ◽  
String Amplitudes ◽  
Closed Bosonic String

We show that a part of logarithmic divergences in the closed bosonic string amplitudes on the disc was over-looked in the previous studies. The sum of all logarithmic divergences is found to be in agreement with the “tadpole” divergences in the effective field theory with the “cosmological term” representing the disc correction. This resolves the problem raised recently by Fischler, Klebanov and Susskind.

scholarly journals Effective field theory approach to modified gravity including Horndeski theory and Hořava–Lifshitz gravity

2014 ◽  
Vol 23 (13) ◽  
pp. 1443008 ◽  
Author(s):  
Ryotaro Kase ◽  
Shinji Tsujikawa
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Modified Gravity ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Power Spectra ◽  
Effective Field ◽  
Theory Approach ◽  
Gravitational Theories ◽  
Wide Range

In this paper, we review the effective field theory of modified gravity in which the Lagrangian involves three-dimensional geometric quantities appearing in the 3+1 decomposition of spacetime. On the flat isotropic cosmological background, we expand a general action up to second-order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories — including Horndeski theory/its recent generalizations and the projectable/nonprojectable versions of Hořava–Lifshitz gravity. We derive the equations of motion for linear cosmological perturbations and apply them to the calculations of inflationary power spectra as well as the dark energy dynamics in Galileon theories. We also show that our general results conveniently recover stability conditions of Hořava–Lifshitz gravity already derived in the literature.

GRAVITON AMPLITUDES, EFFECTIVE ACTION AND STRING GENERATING FUNCTIONAL ON THE DISC

1989 ◽  
Vol 04 (13) ◽  
pp. 3269-3304 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
General Expression ◽  
Effective Field Theory ◽  
Effective Action ◽  
Closed String ◽  
Effective Field ◽  
Generating Functional ◽  
S Matrix ◽  
String Amplitudes

We discuss some issues related to computation and renormalization of closed string amplitudes and effective action on the disc. The general expression for the O (ln ε) term in the string theory and effective field theory generating functionals for the S matrix is found. It is emphasized that in order to establish the correspondence between the string theory and the effective field theory it is necessary to compare the total coefficients of all (“local” plus “modular” and “N-dependent” plus “N-independent”) infinities present in the amplitudes. The regularized expression for the N=3 graviton amplitude on the disc is explicitly computed and it is suggested that a proper regularization is a key to a resolution of a paradox discussed previously in the literature.

scholarly journals On stringy origin of minimal flavor violation

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Tatsuo Kobayashi ◽  
Hajime Otsuka
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Action ◽  
Effective Field ◽  
Minimal Flavor Violation ◽  
Yukawa Couplings ◽  
Cp Violations ◽  
Flavor Violation ◽  
Zero Modes ◽  
The Standard Model

AbstractWe study the minimal flavor violation in the context of string effective field theory. Stringy selection rules indicate that n-point couplings among fermionic zero-modes and lightest scalar modes in the string effective action are given by a product of Yukawa couplings which are regarded as spurion fields of stringy and geometrical symmetries. Hence, Yukawa couplings determine the dynamics of flavor and CP violations. This observation strongly supports the hypothesis of minimal flavor violation in the Standard Model effective field theory.

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