scholarly journals A non-relativistic limit of NS-NS gravity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
E. A. Bergshoeff ◽  
J. Lahnsteiner ◽  
L. Romano ◽  
J. Rosseel ◽  
C. Şimşek
Keyword(s):  
Scale Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Geometric Constraints ◽  
Target Space ◽  
Kinetic Term ◽  
Scale Invariant ◽  
Relativistic Limit ◽  
Cartan Geometry ◽  
Form Field

Abstract We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

scholarly journals Non-relativistic ten-dimensional minimal supergravity

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
E. A. Bergshoeff ◽  
J. Lahnsteiner ◽  
L. Romano ◽  
J. Rosseel ◽  
C. Şimşek
Keyword(s):  
Equations Of Motion ◽  
Local Scale ◽  
Point Of View ◽  
Geometric Constraints ◽  
Relativistic Limit ◽  
Cartan Geometry ◽  
Yang Mills ◽  
The Poisson Equation ◽  
Minimal Supergravity ◽  
Supergravity Action

Abstract We construct a non-relativistic limit of ten-dimensional $$ \mathcal{N} $$ N = 1 supergravity from the point of view of the symmetries, the action, and the equations of motion. This limit can only be realized in a supersymmetric way provided we impose by hand a set of geometric constraints, invariant under all the symmetries of the non-relativistic theory, that define a so-called ‘self-dual’ Dilatation-invariant String Newton-Cartan geometry. The non-relativistic action exhibits three emerging symmetries: one local scale symmetry and two local conformal supersymmetries. Due to these emerging symmetries the Poisson equation for the Newton potential and two partner fermionic equations do not follow from a variation of the non-relativistic action but, instead, are obtained by a supersymmetry variation of the other equations of motion that do follow from a variation of the non-relativistic action. We shortly discuss the inclusion of the Yang-Mills sector that would lead to a non-relativistic heterotic supergravity action.

FLAT CURRENTS OF A GREEN–SCHWARZ SIGMA MODEL ON SUPERCOSET TARGETS WITH ℤ4m GRADING

2008 ◽  
Vol 23 (25) ◽  
pp. 4219-4243 ◽  
Author(s):  
SAN-MIN KE ◽  
KANG-JIE SHI ◽  
CHUN WANG
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Parameter Family ◽  
Target Space ◽  
Suitable Choice ◽  
Kinetic Term ◽  
Classical Solutions ◽  
Virasoro Constraint ◽  
The One

We construct actions of Green–Schwarz sigma models on supercoset targets with ℤ4m grading whose kinetic terms only contain the target-space bosons. We consider a simple case of such kinetic term and show that there exist a one-parameter family of flat currents of the model by requiring a suitable choice of the Wess–Zumino term. Such flat currents naturally lead to a hierarchy of classical conserved nonlocal charges. We also find that the one-parameter flat currents of the model satisfy equations of motion and the Virasoro constraint. This implies that one can generate a series of classical solutions from an existing one. When m = 1, our model coincides with the well-known model given by Metsaev and Tseytlin on a supercoset PSU (2, 2|4)/[ SO (4, 1) × SO (5)] and similar models.

scholarly journals MOND theory

2015 ◽  
Vol 93 (2) ◽  
pp. 107-118 ◽  
Author(s):  
Mordehai Milgrom
Keyword(s):  
Gravitational Lensing ◽  
Scale Invariance ◽  
Equations Of Motion ◽  
Effective Theory ◽  
Special Role ◽  
Scale Invariant ◽  
Limited Applicability ◽  
Total Action ◽  
General Aspects ◽  
Effective Theories

A general account of modified Newtonian dynamics (MOND) theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration — below an acceleration constant a0 — where dynamics become scale invariant. I list some of the salient predictions of these tenets. The special role of a0 and its significance are then discussed. In particular, I stress its coincidence with cosmologically relevant accelerations, which may point to MOND having deep interplay with cosmology. The deep-MOND limit and the consequences of its scale invariance are considered in some detail. There are many ways to achieve scale invariance of the equations of motion — guaranteed if the total action has a well-defined scaling dimension. The mere realization that this is enough to ensure MOND phenomenology opens a wide scope for constructing MOND theories. General aspects of MOND theories are then described, after which I list briefly presently known theories, both nonrelativistic and relativistic. With few exceptions, the construction of known, full-fledged theories follows the same rough pattern: they modify the gravitational action; hinge on a0; introduce, already at the level of the action, an interpolating function between the low and high accelerations; and they obey MOND requirements in the two opposite limits. These theories have much heuristic value as proofs of various concepts (e.g., that covariant MOND theories can be written with correct gravitational lensing). But, probably, none points to the final MOND theory. At best, they are effective theories of limited applicability. I argue that we have so far explored only a small corner of the space of possible MOND theories. I then outline several other promising approaches to constructing MOND theories that strive to obtain MOND as an effective theory from deeper concepts, for example, by modifying inertia and (or) gravity as a result of interactions with some omnipresent agent. These have made encouraging progress in various degrees, but have not yet resulted in full-fledged theories that can be applied to all systems and situations. Some of the presently known theories do enjoy a natural appearance of a cosmological-constant-like contribution that, furthermore, exhibits the observed connection with a0. However, none were shown to address fully the mass discrepancies in cosmology and structure formation that are otherwise explained by cosmological dark matter. This may well be due to our present ignorance of the true connections between MOND and cosmology. We have no clues as to whether and how MOND aspects enter nongravitational phenomena, but I discuss briefly some possibilities.

scholarly journals SSB OF SCALE SYMMETRY, FERMION FAMILIES AND QUINTESSENCE WITHOUT THE LONG-RANGE FORCE PROBLEM

2002 ◽  
Vol 17 (03) ◽  
pp. 417-433 ◽  
Author(s):  
E. I. GUENDELMAN ◽  
A. B. KAGANOVICH
Keyword(s):  
Particle Physics ◽  
Scale Invariance ◽  
Field Potential ◽  
Momentum Tensor ◽  
Kinetic Term ◽  
Exponential Potential ◽  
Scale Invariant ◽  
Fermion Masses ◽  
First Choice ◽  
Scaling Solution

We study a scale-invariant two measures theory where a dilaton field ϕ has no explicit potentials. The scale transformations include the translation of a dilaton ϕ→ϕ+ const . The theory demonstrates a new mechanism for generation of the exponential potential: in the conformal Einstein frame (CEF), after SSB of scale invariance, the theory develops the exponential potential and, in general, the nonlinear kinetic term is generated as well. The scale symmetry does not allow the appearance of terms breaking the exponential shape of the potential that solves the problem of the flatness of the scalar field potential in the context of quintessential scenarios. As examples, two different possibilities for the choice of the dimensionless parameters are presented where the theory permits to get interesting cosmological results. For the first choice, the theory has standard scaling solutions for ϕ usually used in the context of the quintessential scenario. For the second choice, the theory allows three different solutions, one of which is a scaling solution with equation of state pϕ=wρϕ where w is predicted to be restricted by -1<w<-0.82. The regime where the fermionic matter dominates (as compared to the dilatonic contribution) is analyzed. There it is found that starting from a single fermionic field we obtain exactly three different types of spin 1/2 particles in CEF that appears to suggest a new approach to the family problem of particle physics. It is automatically achieved that for two of them, fermion masses are constants, the energy–momentum tensor is canonical and the "fifth force" is absent. For the third type of particles, a fermionic self-interaction appears as a result of SSB of scale invariance.

scholarly journals NONLINEAR SIGMA MODEL ON CONIFOLDS

2002 ◽  
Vol 17 (09) ◽  
pp. 517-533 ◽  
Author(s):  
R. PARTHASARATHY ◽  
K. S. VISWANATHAN
Keyword(s):  
Sigma Model ◽  
Equations Of Motion ◽  
Target Space ◽  
Warp Factor ◽  
Nonlinear Sigma Model ◽  
Explicit Solutions ◽  
Type Ii ◽  
Ricci Flat ◽  
Complex Dimension ◽  
Gauge Connection

Explicit solutions to the conifold equations with complex dimension n = 3, 4 in terms of complex coordinates (fields) are employed to construct the Ricci-flat Kähler metrics on these manifolds. The Kähler two-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of two-dimensional nonlinear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the "integration constants", arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be non-singular. As the target space is Ricci-flat, the perturbative one-loop counterterms being absent, the model becomes topological. The inherent U(1) fiber over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action for a nonlinear sigma model with resolved conifold as target space, is found to have a minimum value, which is topological. The metric is expressed in terms of the six real coordinates and compared with earlier works. The harmonic function, which is the warp factor in Type II-B string theory, is obtained and the ten-dimensional warped metric has the AdS5 × X5 geometry.

scholarly journals LOOP VARIABLES AND THE (FREE) OPEN STRING IN A CURVED BACKGROUND

2005 ◽  
Vol 20 (04) ◽  
pp. 227-242 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Sigma Model ◽  
Equations Of Motion ◽  
Flat Space ◽  
Open String ◽  
Target Space ◽  
Systematic Method ◽  
Curved Space ◽  
Generally Covariant ◽  
Space Equation

Using the loop variable formalism as applied to a sigma model in curved target space, we give a systematic method for writing down gauge and generally covariant equations of motion for the modes of the free open string in curved space. The equations are obtained by covariantizing the flat space equation and then demanding gauge invariance, which introduces additional curvature couplings. As an illustration of the procedure, the spin-two case is worked out explicitly.

scholarly journals Long way to Ricci flatness

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jin Chen ◽  
Chao-Hsiang Sheu ◽  
Mikhail Shifman ◽  
Gianni Tallarita ◽  
Alexei Yung
Keyword(s):  
Sigma Model ◽  
Ultra Violet ◽  
The Other ◽  
Target Space ◽  
Linear Sigma Model ◽  
Close Relative ◽  
Two Dimensional ◽  
World Sheet ◽  
Ricci Flat ◽  
The World

Abstract We study two-dimensional weighted $$ \mathcal{N} $$ N = (2) supersymmetric ℂℙ models with the goal of exploring their infrared (IR) limit. 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) are simplified versions of world-sheet theories on non-Abelian strings in four-dimensional $$ \mathcal{N} $$ N = 2 QCD. In the gauged linear sigma model (GLSM) formulation, 𝕎ℂℙ(N,$$ \tilde{N} $$ N ˜ ) has N charges +1 and $$ \tilde{N} $$ N ˜ charges −1 fields. As well-known, at $$ \tilde{N} $$ N ˜ = N this GLSM is conformal. Its target space is believed to be a non-compact Calabi-Yau manifold. We mostly focus on the N = 2 case, then the Calabi-Yau space is a conifold. On the other hand, in the non-linear sigma model (NLSM) formulation the model has ultra-violet logarithms and does not look conformal. Moreover, its metric is not Ricci-flat. We address this puzzle by studying the renormalization group (RG) flow of the model. We show that the metric of NLSM becomes Ricci-flat in the IR. Moreover, it tends to the known metric of the resolved conifold. We also study a close relative of the 𝕎ℂℙ model — the so called zn model — which in actuality represents the world sheet theory on a non-Abelian semilocal string and show that this zn model has similar RG properties.

scholarly journals Scale Invariance, Horizons, and Inflation

2021 ◽  
Author(s):  
Andre Maeder ◽  
Vesselin G Gueorguiev
Keyword(s):  
Scalar Field ◽  
Scale Invariance ◽  
Maxwell Equations ◽  
High Redshift ◽  
Empty Space ◽  
Causal Connection ◽  
Cosmological Constant Problem ◽  
Scale Invariant ◽  
Starting Point ◽  
Final Answer

Abstract Maxwell equations and the equations of General Relativity are scale invariant in empty space. The presence of charge or currents in electromagnetism or the presence of matter in cosmology are preventing scale invariance. The question arises on how much matter within the horizon is necessary to kill scale invariance. The scale invariant field equation, first written by Dirac in 1973 and then revisited by Canuto et al. in 1977, provides the starting point to address this question. The resulting cosmological models show that, as soon as matter is present, the effects of scale invariance rapidly decline from ϱ = 0 to ϱc, and are forbidden for densities above ϱc. The absence of scale invariance in this case is consistent with considerations about causal connection. Below ϱc, scale invariance appears as an open possibility, which also depends on the occurrence of in the scale invariant context. In the present approach, we identify the scalar field of the empty space in the Scale Invariant Vacuum (SIV) context to the scalar field ϕ in the energy density $\varrho = \frac{1}{2} \dot{\varphi }^2 + V(\varphi )$ of the vacuum at inflation. This leads to some constraints on the potential. This identification also solves the so-called “cosmological constant problem”. In the framework of scale invariance, an inflation with a large number of e-foldings is also predicted. We conclude that scale invariance for models with densities below ϱc is an open possibility; the final answer may come from high redshift observations, where differences from the ΛCDM models appear.

scholarly journals Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Grgur Šimunić
Keyword(s):  
Sigma Models ◽  
Sigma Model ◽  
Target Space ◽  
Two Dimensional ◽  
Courant Algebroids ◽  
Dirac Structures ◽  
Courant Algebroid ◽  
Abelian Case ◽  
Jacobi Manifolds ◽  
Jacobi Structure

Abstract We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.

scholarly journals HETEROTIC T-DUALITY AND THE RENORMALIZATION GROUP

1999 ◽  
Vol 14 (14) ◽  
pp. 2257-2271 ◽  
Author(s):  
KASPER OLSEN ◽  
RICARDO SCHIAPPA
Keyword(s):  
Renormalization Group ◽  
Sigma Models ◽  
Sigma Model ◽  
Beta Function ◽  
Target Space ◽  
Loop Order ◽  
Duality Transformations ◽  
Duality Symmetry ◽  
The One ◽  
Renormalization Group Flows

We consider target space duality transformations for heterotic sigma models and strings away from renormalization group fixed points. By imposing certain consistency requirements between the T-duality symmetry and renormalization group flows, the one-loop gauge beta function is uniquely determined, without any diagram calculations. Classical T-duality symmetry is a valid quantum symmetry of the heterotic sigma model, severely constraining its renormalization flows at this one-loop order. The issue of heterotic anomalies and their cancellation is addressed from this duality constraining viewpoint.

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