Noether identities, β-functions and symmetries in DFT

2019 ◽  
Vol 34 (35) ◽  
pp. 1950234
Author(s):  
J. Antonio García ◽  
R. Abraham Sánchez-Isidro
Keyword(s):  
Effective Action ◽  
Equations Of Motion ◽  
Conformal Symmetry ◽  
Riemann Tensor ◽  
Closed String ◽  
Space Time ◽  
Differential Identities ◽  
Bianchi Identities ◽  
Starting Point ◽  
Strength Formula

Given the [Formula: see text] functions of the closed string sigma model up to one loop in [Formula: see text], the effective action implements the condition [Formula: see text] to preserve conformal symmetry at quantum level. One of the more powerful and striking results of string theory is that this effective action contains Einstein gravity as an emergent dynamics in space–time. We show from the [Formula: see text] functions and its relation with the equations of motion of the effective action that the differential identities are the Noether identities associated with the effective action and its gauge symmetries. From here, we reconstruct the gauge and space–time symmetries of the effective action. In turn, we can show that the differential identities are the contracted Bianchi identities of the field strength [Formula: see text] and Riemann tensor [Formula: see text]. Next, we apply the same ideas to DFT. Taking as starting point that the generalized [Formula: see text] functions in DFT are proportional to the equations of motion, we construct the generalized differential identities in DFT. Relating the Noether identities with the contracted Bianchi identities of DFT, we were able to reconstruct the generalized gauge and space–time symmetries. Finally, we recover the original [Formula: see text] functions, effective action, differential identities, and symmetries when we turn off the [Formula: see text] space–time coordinates from DFT.

scholarly journals A TOY MODEL OF CLOSED STRING TACHYON EFFECTIVE ACTION

2005 ◽  
Vol 20 (07) ◽  
pp. 1481-1493
Author(s):  
J. KLUSOŇ
Keyword(s):  
Exact Solution ◽  
String Theory ◽  
Effective Action ◽  
Flat Space ◽  
Closed String ◽  
Space Time ◽  
Bosonic String ◽  
Two Dimensional ◽  
Linear Dilaton ◽  
Bosonic String Theory

In this paper we propose the toy model of the closed string tachyon effective action that has marginal tachyon profile as its exact solution in case of constant or linear dilaton background. Then we will apply this model for description of two-dimensional bosonic string theory. We will find that the background configuration with the spatial dependent linear dilaton, flat space–time metric and marginal tachyon profile is the exact solution of our model even if we take into account backreaction of tachyon on dilaton and on metric.

EQUIVALENCE OF THE STRING EQUATIONS OF MOTION AND THE σ-MODEL WEYL-INVARIANCE CONDITIONS AT ORDER α′2: DEPENDENCE ON THE DILATON FIELD

1991 ◽  
Vol 06 (28) ◽  
pp. 5099-5125 ◽  
Author(s):  
M.C. BENTO ◽  
O. BERTOLAMI ◽  
J.C. ROMÃO
Keyword(s):  
String Theory ◽  
Effective Action ◽  
Equations Of Motion ◽  
Closed String ◽  
Dilaton Field ◽  
Weyl Invariance ◽  
Field Redefinition ◽  
The Way

We study the structure of effective actions of closed-string theory at order α′2, when the dilaton field is included. We show, in particular, that the way field-redefinition ambiguities are fixed at order a’ affects the order-α′2 results, and find that, as a consequence, different forms for the effective action existing in the literature are in fact equivalent. We discuss the implications of our results for the conjectured relationship between string equations of motion and σ-model β functions.

ONE-LOOP FINITE TEMPERATURE EFFECTIVE ACTION FOR COMPOSITE FIELDS IN CURVED SPACE

1995 ◽  
Vol 10 (03) ◽  
pp. 389-420
Author(s):  
J. BALAKRISHNAN
Keyword(s):  
Effective Action ◽  
Riemann Tensor ◽  
Space Time ◽  
Gauge Condition ◽  
Zero Temperature ◽  
De Sitter ◽  
Abelian Gauge ◽  
Curved Space ◽  
Background Space ◽  
The One

We obtain high temperature results for the one-loop effective action for composite fields in interaction with an Abelian gauge field and minimally coupled to gravity in a curved background space-time, using the Vilkovisky-DeWitt approach, by making a local expansion in the Riemann tensor and its derivatives. We also give results for the fields minimally coupled to gravity in an arbitrary curved background space-time at zero temperature, and for the case where the fields are nonminimally coupled to gravity in Euclidean de Sitter space. The results obtained are gauge-invariant and gauge-condition-independent on-shell as well as off-shell.

scholarly journals A brief review of E theory

2016 ◽  
Vol 31 (26) ◽  
pp. 1630043 ◽  
Author(s):  
Peter West
Keyword(s):  
Infinite Number ◽  
Equations Of Motion ◽  
Space Time ◽  
Unified Theory ◽  
Dynamical Equations ◽  
Supergravity Theory ◽  
Maximal Supergravity ◽  
Abdus Salam ◽  
Strings And Branes ◽  
Time Lead

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

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 Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion

2000 ◽  
Vol 479 (4) ◽  
pp. 411-420 ◽  
Author(s):  
J.A. Helayel-Neto ◽  
A. Penna-Firme ◽  
I.L. Shapiro
Keyword(s):  
Effective Action ◽  
Conformal Symmetry ◽  
Scalar Gravity

Constrained optimal terrain following/threat avoidance trajectory planning using network flow

2014 ◽  
Vol 118 (1203) ◽  
pp. 523-539 ◽  
Author(s):  
R. Zardashti ◽  
A. A. Nikkhah ◽  
M. J. Yazdanpanah
Keyword(s):  
Cost Function ◽  
Trajectory Planning ◽  
Network Flow ◽  
Equations Of Motion ◽  
Minimum Cost ◽  
Masking Effect ◽  
Search Problem ◽  
Starting Point ◽  
Terrain Following ◽  
Threat Avoidance

AbstractThis paper focuses on the trajectory planning for a UAV on a low altitude terrain following/threat avoidance (TF/TA) mission. Using a grid-based approximated discretisation scheme, the continuous constrained optimisation problem into a search problem is transformed over a finite network. A variant of the Minimum Cost Network Flow (MCNF) to this problem is then applied. Based on using the Digital Terrain Elevation Data (DTED) and discrete dynamic equations of motion, the four-dimensional (4D) trajectory (three spatial and one time dimensions) from a starting point to an end point is obtained by minimising a cost function subject to dynamic and mission constraints of the UAV. For each arc in the grid, a cost function is considered as the combination of the arc length, fuel consumption and flight time. The proposed algorithm which considers dynamic and altitude constraints of the UAV explicitly is then used to obtain the feasible trajectory. The resultant trajectory can increase the survivability of the UAV using the threat region avoidance and the terrain masking effect. After obtaining the feasible trajectory, an improved algorithm is proposed to smooth the trajectory. The numeric results are presented to verify the capability of the proposed approach to generate admissible trajectory in minimum possible time in comparison to the previous works.

GEOMETRICAL CONSTRAINTS FOR D = 10, N = 1 SUPERGRAVITY

1989 ◽  
Vol 04 (15) ◽  
pp. 3819-3831 ◽  
Author(s):  
LING-LIE CHAU ◽  
CHONG-SA LIM
Keyword(s):  
Equations Of Motion ◽  
Bianchi Identities ◽  
Dynamical Consequence ◽  
Integrability Conditions ◽  
Geometrical Constraints ◽  
Additional Constraints

A set of geometrical constraints for D = 10, N = 1 supergravity is formulated. It has the meaning as integrability conditions on "hyperplanes" determined by light-like lines in the superspace. The dynamical consequence of these geometrical constraints is studied via Bianchi identities. Since no equations of motion have resulted, these geometrical constraints can form an off-shell set of constraints for the theory. We also discuss additional constraints that lead to Poincare supergravity equations of motion. The relation of the theory with D = 4 N = 4 supergravity is also illuminated.

SPECTRAL FLOW AND FREE FIELD REALIZATIONS OF BOSONIC STRINGS ON NAPPI–WITTEN GROUP MANIFOLD

2011 ◽  
Vol 26 (01) ◽  
pp. 149-160
Author(s):  
GANG CHEN
Keyword(s):  
Lie Algebra ◽  
Bosonic Strings ◽  
Free Field ◽  
Geometric Interpretation ◽  
Closed String ◽  
Space Time ◽  
Spectral Flow ◽  
Affine Lie Algebra ◽  
Group Manifold ◽  
Free Field Realization

In this paper we study some aspects of closed string theories in the Nappi–Witten space–time. The effects of spectral flow on the geodesics are studied in terms of an explicit parametrization of the group manifold. The worldsheets of the closed strings under the spectral flow of the geodesics can be classified into four classes, each with a geometric interpretation. We also obtain a free field realization of the Nappi–Witten affine Lie algebra in the most general conditions using a different but equivalent parametrization of the group manifold.

ANOMALY FREE SUPERGRAVITY IN D=10: I) THE BIANCHI IDENTITIES AND THE BOSONIC LAGRANGIAN

1988 ◽  
Vol 03 (04) ◽  
pp. 953-1021 ◽  
Author(s):  
RICCARDO D’AURIA ◽  
PIETRO FRÉ ◽  
MARIO RACITI ◽  
FRANCO RIVA
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Variational Equation ◽  
Second Order ◽  
Effective Theory ◽  
Spin Connection ◽  
Bianchi Identities ◽  
First Order ◽  
Interaction Terms ◽  
Starting Point

Using a theorem by Bonora-Pasti and Tonin on the existence of a solution for D=10N=1 Bianchi identities in the presence of a Lorentz Chern Simons term, we find an explicit parametrization of the superspace curvatures. Our solution depends only on one free parameter which can be reabsorbed in a field redefinition of the dilaton and of the gravitello. We emphasize that the essential point which enables us to obtain a closed form for the curvature parametrizations and hence for the supersymmetry transformation rules is the use of first order formalism. The spin connection is known once the torsion is known. This latter, rather than being identified with Hµνρ as it is usually done in the literature, is related to it by a differential equation which reduces to the algebraic relation Hµνρ = - 3Tµνρ e4/3σ only at γ1=0 (γ1 being proportional to κ/g2). The solution of the Bianchi identities exhibited in this paper corresponds to a D=10 anomaly free supergravity (AFS). This theory is unique in first order formalism but corresponds to various theories in second order formalism. Indeed the torsion equation is a differential equation which, in order to be solved must be supplemented with boundary conditions. One wonders whether supplemented with a judicious choice of boundary conditions for the torsion equation, AFS yields all the interaction terms found in the effective theory of the heterotic string (ETHS). In this respect two remarks are in order. Firstly it appears that solving the torsion equation iteratively with Tµνρ = -1/3Hµνρ e-4/3σ as starting point all the terms of ETHS except those with a ζ(3) coefficient show up. (Whether the coefficient agree is still to be checked.) Secondly, as shown in this paper the rheonomic solution of the super Poincaré Bianchi identities is unique. Hence additional interaction terms can be added to the Lagrangian only by modifying the rheonomic parametrization of the [Formula: see text]-curvature. The only assumption made in our paper is that [Formula: see text] has at most ψ∧ψ∧V components (sector (1,2)). Correspondingly the only room left for a modification of the present theory is the addition of a (0, 3) part in the rheonomic parametrization of [Formula: see text]. When this work was already finished a conjecture was published by Lechner Pasti and Tonin that such a generalization of AFS might exist and be responsible for the ζ(3) missing term. Indeed if we were able to solve the [Formula: see text]-Bianchi with this new (0, 3)-part then the torsion equation would be modified via new terms which, in second order formalism, lead to additional gravitational interactions. The equation of motion of Anomaly Free Supergravity can be worked out from the Bianchi identities: we indicate through which steps. The corresponding Lagrangian could be constructed with the standard procedures of the rheonomy approach. In this paper we limit ourselves to the bosonic sector of such a Lagrangian and we show that it can indeed be constructed in such a way as to produce the relation between Hµνρ and Tµνρ as a variational equation.

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