scholarly journals Classical and tree-level approaches to gravitational deflection in higher-derivative gravity

2015 ◽  
Vol 91 (12) ◽  
Author(s):  
Antonio Accioly ◽  
José Helayël-Neto ◽  
Breno Giacchini ◽  
Wallace Herdy
Keyword(s):  
Tree Level ◽  
Higher Derivative ◽  
Gravitational Deflection

scholarly journals Composing effective prediction at five points

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Joseph M. Carrasco ◽  
Laurentiu Rodina ◽  
Suna Zekioğlu
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitude ◽  
Building Blocks ◽  
Tree Level ◽  
Critical Aspect ◽  
Higher Derivative ◽  
Higher Dimensional ◽  
Single Trace ◽  
The Relationship ◽  
Double Copy

Abstract Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d4) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

SOLVING THE RIDDLE OF THE INCOMPATIBILITY BETWEEN RENORMALIZABILITY AND UNITARITY IN N-DIMENSIONAL EINSTEIN GRAVITY ENLARGED BY CURVATURE-SQUARED TERMS

2013 ◽  
Vol 22 (12) ◽  
pp. 1342015 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
JOSÉ HELAYËL-NETO ◽  
ESLLEY SCATENA ◽  
RODRIGO TURCATI
Keyword(s):  
Gravitational Potential ◽  
Physical Theory ◽  
Einstein Gravity ◽  
Simple Solution ◽  
Tree Level ◽  
Main Argument ◽  
Higher Derivative

One of the puzzling aspects of N-dimensional Einstein Gravity (NDEG) augmented by curvature-squared terms is why renormalizability and unitarity, two of the most important properties of any physical theory, cannot be reconciled in its framework. Actually, the reason why these properties are mutually incompatible within the context of generic higher-derivative models, not necessarily related to gravity, is one of the unsolved mysteries of physics. Here, a simple solution to the NDEG riddle, based on the analysis of the interparticle gravitational potential, is presented. The main argument used to support our discussion is that tree-level unitarity and the existence of a singularity in the potential are intertwined.

scholarly journals UNAVOIDABLE CONFLICT BETWEEN MASSIVE GRAVITY MODELS AND MASSIVE TOPOLOGICAL TERMS

2004 ◽  
Vol 19 (11) ◽  
pp. 817-826 ◽  
Author(s):  
ANTONIO ACCIOLY ◽  
MARCO DIAS
Keyword(s):  
Three Dimensional ◽  
Massive Gravity ◽  
Ricci Scalar ◽  
Gravity Models ◽  
Tree Level ◽  
Common Belief ◽  
Higher Derivative ◽  
The Common ◽  
Chern Simons ◽  
Topological Term

Massive gravity models in (2+1) dimensions, such as those obtained by adding to Einstein's gravity the usual Fierz–Pauli, or the more complicated Ricci scalar squared (R2), terms, are tree level unitary. Interesting enough these seemingly harmless systems have their unitarity spoiled when they are augmented by a Chern–Simons term. Furthermore, if the massive topological term is added to [Formula: see text] gravity, or to [Formula: see text] gravity (higher-derivative gravity), which are nonunitary at the tree level, the resulting models remain nonunitary. Therefore, unlike the common belief, as well as the claims in the literature, the coexistence between three-dimensional massive gravity models and massive topological terms is conflicting.

INFLATION FROM THE SUPERSTRING VACUUM

2009 ◽  
Vol 24 (20n21) ◽  
pp. 4021-4037
Author(s):  
M. D. POLLOCK
Keyword(s):  
Background Radiation ◽  
Physical Space ◽  
Reduction Process ◽  
Tree Level ◽  
Internal Space ◽  
De Sitter ◽  
Superstring Theory ◽  
Higher Derivative ◽  
Effective Lagrangian ◽  
Microwave Background Radiation

Quartic higher-derivative gravitational terms in the effective Lagrangian of the heterotic superstring theory renormalize the bare, four-dimensional gravitational coupling [Formula: see text], due to the reduction process [Formula: see text], according to the formula [Formula: see text], where A r and B r are the moduli for the physical space gij(xk) and internal space [Formula: see text], respectively. The Euler characteristic [Formula: see text] is negative for a three-generation Calabi–Yau manifold, and therefore both the additional terms, of tree-level and one-loop origin, produce a decrease in κ-2, which changes sign when κ-2 = 0. The corresponding tree-level critical point is [Formula: see text], if we set [Formula: see text] and λ = 15π2, for compactification onto a torus. Values [Formula: see text] yield the anti-gravity region κ-2 < 0, which is analytically accessible from the normal gravity region κ-2 > 0. The only non-singular, vacuum minimum of the potential [Formula: see text] is located at the point [Formula: see text], where [Formula: see text], the quadratic trace anomaly [Formula: see text] dominates over [Formula: see text], and a phase of de Sitter expansion may occur, as first envisaged by Starobinsky, in approximate agreement with the constraint due to the effect of gravitational waves upon the anisotropy of the cosmic microwave background radiation. There is no non-singular minimum of the potential [Formula: see text].

scholarly journals D-INSTANTON CORRECTIONS AS (p, q)-STRING EFFECTS AND NONRENORMALIZATION THEOREMS

1998 ◽  
Vol 13 (29) ◽  
pp. 5075-5092 ◽  
Author(s):  
A. KEHAGIAS ◽  
H. PARTOUCHE
Keyword(s):  
String Theory ◽  
Perturbative Expansion ◽  
Point Of View ◽  
Tree Level ◽  
Higher Derivative ◽  
M Theory

We discuss higher derivative interactions in the type IIB superstring in ten dimensions. From the fundamental stri ng point of view, the nonperturbative corrections are due to D-instantons. We argue that they can alternatively be understood as arising from (p, q)-strings. We derive a nonrenormalization theorem for eight-derivative bosonic interactions, which states that terms involving either NS–NS or R–R fields occur at tree-level and one-loop only. By using the SL(2, Z) symmetry of M theory on T2, we show that in order for the possible R3m+1 (m = 1, 2, …) interactions in M theory to have a consistent perturbative expansion in nine dimensions, m must be odd. Thus, only R6N+4 (N = 0,1, …) terms can be present in M theory and their string theory counterparts arise at N and 2N + 1 loops. Finally, we treat an example of fermionic term.

scholarly journals Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Junho Hong ◽  
James T. Liu
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Gauge Theories ◽  
Fermi Gas ◽  
Tree Level ◽  
Saddle Point Approximation ◽  
Higher Derivative ◽  
The Matrix ◽  
Hooft Limit ◽  
Chern Simons

Abstract We investigate the S3 free energy of $$ \mathcal{N} $$ N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N)r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = − log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal $$ \frac{1}{6} $$ 1 6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

scholarly journals Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Tobias Hansen
Keyword(s):  
Gauge Group ◽  
Flat Space ◽  
Closed Form Expression ◽  
Tree Level ◽  
Modular Invariant ◽  
Higher Derivative ◽  
S Matrix ◽  
Space Limit ◽  
Type Iib String Theory ◽  
General Gauge

Abstract We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

RENORMALIZATION EFFECTS IN THE SUPERSTRING MODULI FROM THE HIGHER-DERIVATIVE TERMS

2001 ◽  
Vol 16 (19) ◽  
pp. 3217-3235 ◽  
Author(s):  
M. D. POLLOCK
Keyword(s):  
Equation Of State ◽  
Kinetic Energy ◽  
Canonical Form ◽  
Dimensional Reduction ◽  
Scalar Fields ◽  
Adiabatic Index ◽  
Einstein Metric ◽  
Tree Level ◽  
Superstring Theory ◽  
Higher Derivative

The dimensional reduction of the effective ten-action [Formula: see text] of the heterotic superstring theory to the physical four-action S[gij] results in the appearance of three moduli B(a), whose real parts [Formula: see text], set equal for simplicity, define the radius and shape of the compact internal six-space [Formula: see text], in addition to the dilaton [Formula: see text], the ten-interval being [Formula: see text]. These scalar fields are massless at tree level and can be put into canonical form with coefficients [Formula: see text] for the positive kinetic-energy terms, when higher-derivative terms are ignored, as found by Witten, so that [Formula: see text]. Previously, we have shown that σA and σB acquire a potential from the higher-derivative terms [Formula: see text] and [Formula: see text], which becomes large close to the Planck era. Here, we discuss the renormalization of the kinetic-energy terms due to [Formula: see text] which, after diagonalization, results in a mixing of ∇σB with ∇σA, while the remaining coefficient of (∇σB)2 vanishes at t c ≈ t P /12 in a radiation-dominated Universe, corresponding to a temperature T c ≈ 5 × 1017 GeV , where the four-theory is still classical. At earlier times, the energy is unbounded from below, signalling that the four-theory has become unphysical, and that the string must still be in its uncompactified form with one dilaton ϕ, whose canonical kinetic energy is positive in the Einstein metric. This mechanism depends upon the equation of state of the source for the Friedmann expansion assumed, and is only effective for values of the adiabatic index in the range 1.14 < γ < 2.63, which thus includes radiation (γ = 4/3) and the Zel'dovich equation of state (γ = 2).

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