scholarly journals Galileon string measure and other modified measure extended objects

2017 ◽  
Vol 32 (38) ◽  
pp. 1750211 ◽  
Author(s):  
T. O. Vulfs ◽  
E. I. Guendelman
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Equations Of Motion ◽  
String Tension ◽  
Gauge Transformations ◽  
Higher Derivative ◽  
Dynamical Degree ◽  
Integration Measure ◽  
Definition Of ◽  
Galileon Field

We show that it is possible to formulate string theory as a “Galileon string theory”. The Galileon field [Formula: see text] enters in the definition of the integration measure in the action. Following the methods of the modified measure string theory, we find that the final equations are again those of the sigma-model. Moreover, the string tension appears again as an additional dynamical degree of freedom. At the same time, the theory satisfies all requirements of the Galileon higher derivative theory at the action level while the equations of motion are still of the second-order. A Galileon symmetry is displayed explicitly in the conformal string worldsheet frame. Also, we define the Galileon gauge transformations. Generalizations to branes with other modified measures are discussed.

SIGMA MODEL APPROACH TO STRING THEORY

1989 ◽  
Vol 04 (06) ◽  
pp. 1257-1318 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
String Theory ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Tree Approximation ◽  
Massless Fields ◽  
Model Approach

A review of the σ-model approach to derivation of effective string equations of motion for the massless fields is presented. We limit our consideration to the case of the tree approximation in the closed Bose string theory.

scholarly journals LOOP VARIABLES AND GAUGE INVARIANCE IN (OPEN) BOSONIC STRING THEORY

2002 ◽  
Vol 17 (18) ◽  
pp. 1175-1190 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
String Theory ◽  
Gauge Invariance ◽  
Equations Of Motion ◽  
Standard Form ◽  
Open String ◽  
Finite Width ◽  
Massive Mode ◽  
Gauge Transformations ◽  
Variable Approach ◽  
Free Case

We give a simplified and more complete description of the loop variable approach for writing down gauge-invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite worldsheet cutoff and that in the ir limit, equivalence with the Callan–Symanzik β-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon–photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite worldsheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into the standard form.

NAMBU–GOTO STRING THEORY ON A SPACE–TIME LATTICE — PLAQUETTE RANDOM SURFACES REVISITED

1993 ◽  
Vol 08 (19) ◽  
pp. 3339-3357
Author(s):  
ROGER DEARNALEY
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Continuum Limit ◽  
Critical Dimension ◽  
String Tension ◽  
Space Time ◽  
Random Surfaces ◽  
Finite Dimensional ◽  
Lattice Approximation ◽  
Definition Of

Two lattice approximations to the Nambu–Goto string using random surfaces constructed from lattice plaquettes are described. The first is well known, and was shown by Eguchi and Kawai to have a sum over histories which is divergent for all values of the bare (i.e. unrenormalized) string tension.1 This result is confirmed, but it is shown that this is not true of the second lattice approximation. Its sum over histories is convergent for all values of the bare string tension above a certain limit, and is proved to be divergent for all values below this limit. If this limit could be shown to give a satisfactory continuum limit, and the model could be proven to be free of anomalies in the critical dimension, it would give us a finite-dimensional local second-quantized path-integral definition of Nambu–Goto string theory.

Implications of the spectrum of dynamically generated string tension theories

2021 ◽  
Author(s):  
E. I. Guendelman
Keyword(s):  
String Theory ◽  
Early Universe ◽  
Conformal Invariance ◽  
Background Field ◽  
String Tension ◽  
Degree Of Freedom ◽  
Relative Sign ◽  
World Sheet ◽  
Dynamical Degree ◽  
The World

The string tension does not have to be put in by hand, it can be dynamically generated, as in the case when we formulate string theory in the modified measure formalism, and other formulations as well. Then string tension appears, but as an additional dynamical degree of freedom. It can be seen however that this string tension is not universal, but rather each string generates its own string tension, which can have a different value for each string. We also define a new Tension scalar background field which change locally the value of the string tension along the world sheets of the strings. When there are many strings with different string tensions this Tension field can be determined from the requirement of world sheet conformal invariance and for two types of string tensions depending on the relative sign of the tensions we obtain nonsingular cosmologies and warp space scenarios and when the two string tensions are positive, we obtain scenarios where the Hagedorn temperature is avoided in the early universe or in regions of warped space time where the string tensions become very big.

scholarly journals Beta functions for the duality-invariant sigma model

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Roberto Bonezzi ◽  
Tomas Codina ◽  
Olaf Hohm
Keyword(s):  
String Theory ◽  
Sigma Models ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Background Field ◽  
Field Method ◽  
Bosonic String ◽  
Two Dimensional ◽  
Background Field Method ◽  
Bosonic String Theory

Abstract The O(d, d) invariant worldsheet theory for bosonic string theory with d abelian isometries is employed to compute the beta functions and Weyl anomaly at one-loop. We show that vanishing of the Weyl anomaly coefficients implies the equations of motion of the Maharana-Schwarz action. We give a self-contained introduction into the required techniques, including beta functions, the Weyl anomaly for two-dimensional sigma models and the background field method. This sets the stage for a sequel to this paper on generalizations to higher loops and α′ corrections.

scholarly journals Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
L. Borsten ◽  
I. Jubb ◽  
V. Makwana ◽  
S. Nagy
Keyword(s):  
Homogeneous Spaces ◽  
Gauge Fields ◽  
Convolution Product ◽  
Tensor Fields ◽  
Einstein Universe ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Static Einstein Universe ◽  
Definition Of ◽  
Gauge Gravity

Abstract A definition of a convolution of tensor fields on group manifolds is given, which is then generalised to generic homogeneous spaces. This is applied to the product of gauge fields in the context of ‘gravity = gauge × gauge’. In particular, it is shown that the linear Becchi-Rouet-Stora-Tyutin (BRST) gauge transformations of two Yang-Mills gauge fields generate the linear BRST diffeomorphism transformations of the graviton. This facilitates the definition of the ‘gauge × gauge’ convolution product on, for example, the static Einstein universe, and more generally for ultrastatic spacetimes with compact spatial slices.

scholarly journals Gauging the higher-spin-like symmetries by the Moyal product

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
M. Cvitan ◽  
P. Dominis Prester ◽  
S. Giaccari ◽  
M. Paulišić ◽  
I. Vuković
Keyword(s):  
Linear Connection ◽  
Covariant Formulation ◽  
Formal Similarity ◽  
Commutative Field ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Higher Derivative ◽  
Novel Approach ◽  
Emergent Geometry ◽  
Higher Spin

Abstract We analyze a novel approach to gauging rigid higher derivative (higher spin) symmetries of free relativistic actions defined on flat spacetime, building on the formalism originally developed by Bonora et al. and Bekaert et al. in their studies of linear coupling of matter fields to an infinite tower of higher spin fields. The off-shell definition is based on fields defined on a 2d-dimensional master space equipped with a symplectic structure, where the infinite dimensional Lie algebra of gauge transformations is given by the Moyal commutator. Using this algebra we construct well-defined weakly non-local actions, both in the gauge and the matter sector, by mimicking the Yang-Mills procedure. The theory allows for a description in terms of an infinite tower of higher spin spacetime fields only on-shell. Interestingly, Euclidean theory allows for such a description also off-shell. Owing to its formal similarity to non-commutative field theories, the formalism allows for the introduction of a covariant potential which plays the role of the generalised vielbein. This covariant formulation uncovers the existence of other phases and shows that the theory can be written in a matrix model form. The symmetries of the theory are analyzed and conserved currents are explicitly constructed. By studying the spin-2 sector we show that the emergent geometry is closely related to teleparallel geometry, in the sense that the induced linear connection is opposite to Weitzenböck’s.

scholarly journals LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

2001 ◽  
Vol 16 (10) ◽  
pp. 1679-1701 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Gauge Transformation ◽  
Dimensional Reduction ◽  
Mass Shell ◽  
Bosonic String ◽  
Higher Dimension ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

scholarly journals On the Dirac eigenvalues as observables of the on-shell N = 2D = 4 Euclidean supergravity

Open Physics ◽  
2008 ◽  
Vol 6 (4) ◽  
Author(s):  
Ion Vancea
Keyword(s):  
Phase Space ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Gauge Transformations

AbstractWe generalize previous works on the Dirac eigenvalues as dynamical variables of Euclidean gravity and N =1 D = 4 supergravity to on-shell N = 2 D = 4 Euclidean supergravity. The covariant phase space of the theory is defined as the space of the solutions of the equations of motion modulo the on-shell gauge transformations. In this space we define the Poisson brackets and compute their value for the Dirac eigenvalues.

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