scholarly journals Consistency of superspace low energy equations of motion of 4D Type II superstring with Type II sigma model at tree-level

2003 ◽  
Vol 573 ◽  
pp. 217-226 ◽  
Author(s):  
D.L. Nedel
Keyword(s):  
Sigma Model ◽  
Equations Of Motion ◽  
Low Energy ◽  
Tree Level ◽  
Type Ii ◽  
Energy Equations

scholarly journals Non-Abelian moduli on domain walls

2014 ◽  
Vol 29 (32) ◽  
pp. 1450193 ◽  
Author(s):  
E. Kurianovych ◽  
M. Shifman
Keyword(s):  
Sigma Model ◽  
Domain Walls ◽  
Cosmic Strings ◽  
Equations Of Motion ◽  
Orbit Interaction ◽  
Low Energy ◽  
Spin Orbit ◽  
Energy Limit ◽  
Wall Profile ◽  
Bulk Parameters

We study a simple model supporting domain walls which possess two orientational moduli in addition to the conventional translational modulus. This model is conceptually close to Witten's cosmic strings. We observe an O(3) sigma model on the wall worldvolume in the low-energy limit. We solve (numerically) classical static equations of motion and find the wall profile functions and the value of the coupling of the O(3) model in terms of the bulk parameters. In the second part a term describing a spin-orbit interaction in the bulk is added, which gives rise to an entanglement between rotational and translational moduli. The corresponding extra term in the low-energy Lagrangian is calculated.

scholarly journals COSMOLOGICAL CONSTANT IN LOW ENERGY d = 4 STRING LEADS TO (STATIC SPHERICALLY SYMMETRIC) NAKED SINGULARITY

1995 ◽  
Vol 10 (10) ◽  
pp. 789-797 ◽  
Author(s):  
S. KALYANA RAMA
Keyword(s):  
Cosmological Constant ◽  
Sigma Model ◽  
Naked Singularity ◽  
Point Of View ◽  
Low Energy ◽  
Tree Level ◽  
Spherically Symmetric ◽  
Naked Singularities ◽  
Noncritical Strings ◽  
Β Function

In the sigma model approach, the β-function equations for noncritical strings contain a term which acts like a tree level cosmological constant, Λ. We analyze the static, spherically symmetric solutions to these equations in d = 4 space-time, which will describe the gravitational field of a point star up to a distance r*, of the order of parsecs. We show that the curvature scalar seen by the strings is singular in these solutions if Λ ≠ 0. This singularity is naked. Requiring its absence up to a distance r* imposes the constraint [Formula: see text] in natural units. Thus if r* ≃ 1 Mpc then |Λ| < 10−114, and if r* extends all the way up to the edge of the universe (1028 cm) then |Λ| < 10−122 in natural units. From another point of view, our analysis implies that low energy d = 4 noncritical strings in the sigma model formulation lead to naked singularities.

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 Covariant color-kinematics duality

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Clifford Cheung ◽  
James Mangan
Keyword(s):  
Sigma Model ◽  
Equations Of Motion ◽  
Explicit Construction ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Yang Mills ◽  
Novel Structure ◽  
Double Copy ◽  
Number Of Particles ◽  
Field Strengths

Abstract We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory.For Yang-Mills (YM) theory, this same approach reveals a novel structure — covariant color-kinematics duality — whose only difference from the conventional duality is that 1/□ is replaced with covariant 1/D2. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an F3 theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and F3 theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background.Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

scholarly journals MANIFESTLY O(d,d) INVARIANT APPROACH TO SPACE-TIME DEPENDENT STRING VACUA

1991 ◽  
Vol 06 (37) ◽  
pp. 3397-3404 ◽  
Author(s):  
K. A. MEISSNER ◽  
G. VENEZIANO
Keyword(s):  
Black Hole ◽  
Renormalization Group ◽  
General Solution ◽  
Equations Of Motion ◽  
Space Time ◽  
Low Energy ◽  
Time Dependent ◽  
Energy Equations ◽  
Invariant Approach ◽  
Black Hole Solutions

An O(d,d) symmetry of the manifold of string vacua that do not depend on d (out of D) space-time coordinates has been recently identified. Here we write down, for d=D-1, the low energy equations of motion and their general solution in a manifestly O(d,d)-invariant form, pointing out an amusing similarity with the renormalization group framework. Previously considered cosmological and black hole solutions are reproduced as particular examples.

scholarly journals Standard Model Effective Potential from Trace Anomalies

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Renata Jora
Keyword(s):  
Higgs Boson ◽  
Standard Model ◽  
Effective Potential ◽  
Sigma Model ◽  
Low Energy ◽  
Boson Mass ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Higgs Boson Mass ◽  
Quantum Level

By analogy with the low energy QCD effective linear sigma model, we construct a standard model effective potential based entirely on the requirement that the tree level and quantum level trace anomalies must be satisfied. We discuss a particular realization of this potential in connection with the Higgs boson mass and Higgs boson effective couplings to two photons and two gluons. We find that this kind of potential may describe well the known phenomenology of the Higgs boson.

scholarly journals Nothing is certain in string compactifications

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Iñaki García Etxebarria ◽  
Miguel Montero ◽  
Kepa Sousa ◽  
Irene Valenzuela
Keyword(s):  
Flux Compactifications ◽  
Spin Structure ◽  
Energy Condition ◽  
Low Energy ◽  
Type Ii ◽  
String Compactifications ◽  
Compact Dimension ◽  
Bordism Group ◽  
Topological Obstruction ◽  
M Theory

Abstract A bubble of nothing is a spacetime instability where a compact dimension collapses. After nucleation, it expands at the speed of light, leaving “nothing” behind. We argue that the topological and dynamical mechanisms which could protect a compactification against decay to nothing seem to be absent in string compactifications once supersymmetry is broken. The topological obstruction lies in a bordism group and, surprisingly, it can disappear even for a SUSY-compatible spin structure. As a proof of principle, we construct an explicit bubble of nothing for a T3 with completely periodic (SUSY-compatible) spin structure in an Einstein dilaton Gauss-Bonnet theory, which arises in the low-energy limit of certain heterotic and type II flux compactifications. Without the topological protection, supersymmetric compactifications are purely stabilized by a Coleman-deLuccia mechanism, which relies on a certain local energy condition. This is violated in our example by the nonsupersymmetric GB term. In the presence of fluxes this energy condition gets modified and its violation might be related to the Weak Gravity Conjecture.We expect that our techniques can be used to construct a plethora of new bubbles of nothing in any setup where the low-energy bordism group vanishes, including type II compactifications on CY3, AdS flux compactifications on 5-manifolds, and M-theory on 7-manifolds. This lends further evidence to the conjecture that any non-supersymmetric vacuum of quantum gravity is ultimately unstable.

scholarly journals On differential operators and unifying relations for 1-loop Feynman integrands

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Kang Zhou
Keyword(s):  
Sigma Model ◽  
Differential Operators ◽  
Linear Sigma Model ◽  
Tree Level ◽  
Maxwell Theory ◽  
Scalar Theory ◽  
Yang Mills ◽  
Loop Level ◽  
Wide Range ◽  
Non Linear

Abstract We generalize the unifying relations for tree amplitudes to the 1-loop Feynman integrands. By employing the 1-loop CHY formula, we construct differential operators which transmute the 1-loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, including Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at 1-loop level is established. Under the well known unitarity cut, the 1-loop level operators will factorize into two tree level operators. Such factorization is also discussed.

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