118969895
The Kinematics of particles moving in rainbow spacetime
The kinematics of massive particles moving in rainbow spacetime is studied. We derive the equation of geodesics when the semiclassical effect of moving particles on the background is taken into account. In particular we show that in rainbow flat spacetime the trajectory of a freely falling particle remains unchanged which is still a straight line in energy-independent coordinate system. The implication to the Unruh effect in rainbow flat spacetime is also discussed.
13895100
C, P, and T of braid excitations in quantum gravity
Abstract We study the discrete transformations of four-valent braid excitations of framed spin networks embedded in a topological three-manifold. We show that four-valent braids allow seven and only seven discrete transformations. These transformations can be uniquely mapped to C, P, T, and their products. Each CPT multiplet of actively-interacting braids is found to be uniquely characterized by a non-negative integer. Finally, braid interactions turn out to be invariant under C, P, and T.
26188456
A link representation for gravity amplitudes
A bstractWe derive a link representation for all tree amplitudes in $ \mathcal{N}=8 $ supergravity, from a recent conjecture by Cachazo and Skinner. The new formula explicitly writes amplitudes as contour integrals over constrained link variables, with an integrand naturally expressed in terms of determinants, or equivalently tree diagrams. Important symmetries of the amplitude, such as supersymmetry, parity and (partial) permutation invariance, are kept manifest in the formulation. We also comment on rewriting the formula in a GL(k)-invariant manner, which may serve as a starting point for the generalization to possible Grassmannian contour integrals.
119227620
Scattering in three dimensions from rational maps
A bstractThe complete tree-level S-matrix of four dimensional $ \mathcal{N}=4 $ super Yang-Mills and $ \mathcal{N}=8 $ supergravity has compact forms as integrals over the moduli space of certain rational maps. In this note we derive formulas for amplitudes in three dimensions by using the fact that when amplitudes are dressed with proper wave functions dimensional reduction becomes straightforward. This procedure leads to formulas in terms of rational maps for three dimensional maximally supersymmetric Yang-Mills and gravity theories. The integrand of the new formulas contains three basic structures: Parke-Taylor-like factors, Vandermonde determinants and resultants. Integrating out some of the Grassmann directions produces formulas for theories with less than maximal supersymmetry, which exposes yet a fourth kind of structure. Combining all four basic structures we start a search for consistent S-matrices in three dimensions. Very nicely, the most natural ones are those corresponding to ABJM and BLG theories. We also make a connection between the power of a resultant in the integrand, representations of the Poincaré group, infrared behavior and conformality of a theory. Extensions to other theories in three dimensions and to arbitrary dimensions are also discussed.
54062406
Scattering equations and matrices: from Einstein to Yang-Mills, DBI and NLSM
A bstractThe tree-level S-matrix of Einstein’s theory is known to have a representation as an integral over the moduli space of punctured spheres localized to the solutions of the scattering equations. In this paper we introduce three operations that can be applied on the integrand in order to produce other theories. Starting in d + M dimensions we use dimensional reduction to construct Einstein-Maxwell with gauge group U(1)M . The second operation turns gravitons into gluons and we call it “squeezing”. This gives rise to a formula for all multi-trace mixed amplitudes in Einstein-Yang-Mills. Dimensionally reducing Yang-Mills we find the S-matrix of a special Yang-Mills-Scalar (YMS) theory, and by the squeezing operation we find that of a YMS theory with an additional cubic scalar vertex. A corollary of the YMS formula gives one for a single massless scalar with a ϕ4 interaction. Starting again from Einstein’s theory but in d + d dimensions we introduce a “generalized dimensional reduction” that produces the Born-Infeld theory or a special Galileon theory in d dimensions depending on how it is applied. An extension of Born-Infeld formula leads to one for the Dirac-Born-Infeld (DBI) theory. By applying the same operation to Yang-Mills we obtain the U(N ) non-linear sigma model (NLSM). Finally, we show how the Kawai-Lewellen-Tye relations naturally follow from our formulation and provide additional connections among these theories. One such relation constructs DBI from YMS and NLSM.
115780520
Scattering equations and Kawai-Lewellen-Tye orthogonality
Several recent developments point to the fact that rational maps from $n$-punctured spheres to the null cone of $D$-dimensional momentum space provide a natural language for describing the scattering of massless particles in $D$ dimensions. In this paper we identify and study equations relating the kinematic invariants ${s}_{ab}$ and the puncture locations ${\ensuremath{\sigma}}_{c}$, which we call the scattering equations. We provide an inductive algorithm in the number of particles for their solutions and prove a remarkable property which we call Kawai--Lewellen--Tye (KLT) orthogonality. In a nutshell, KLT orthogonality means that ``Parke--Taylor'' vectors constructed from the solutions to the scattering equations are mutually orthogonal with respect to the KLT bilinear form. We end with comments on possible connections to gauge theory and gravity amplitudes in any dimension and to the high-energy limit of string theory amplitudes.
32091410
Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs
A bstractWe study Rényi entropy of locally excited states with considering the thermal and boundary effects respectively in two dimensional conformal field theories (CFTs). Firstly, we consider locally excited states obtained by acting primary operators on a thermal state in low temperature limit. The Rényi entropy is summation of contribution from thermal effect and local excitation. Secondly, we mainly study the Rényi entropy of locally excited states in 2D CFT with a boundary. We show that the time evolution of Rényi entropy is affected by the boundary, but does not depend on the boundary condition. Moreover, we show that the maximal value of Rényi entropy always coincides with the log of quantum dimension of the primary operator. In terms of quasi-particle interpretation, the boundary behaves as an infinite potential barrier which reflects any energy moving towards it.
76649422
A hQCD model and its phase diagram in Einstein-Maxwell-Dilaton system
A bstractBy use of the potential reconstruction approach we obtain a series of asymptotically AdS (aAdS) black hole solutions in an Einstein-Maxwell-Dilaton (EMD) system. Basing on the solutions of the system, we reconstruct a semi-analytical holographic QCD (hQCD) model with a quadratic term in warped factor. We discuss some aspects of the hQCD model, in particular we calculate the free energy of two static color sources (a heavy quark-antiquark pair) which is an important order parameter to describe confinement/deconfinement phase transition. The behavior of the free energy with respect to temperature and chemical potential is studied. We find that in the hQCD model the deconfinement phase transition can be realized and a critical point occurs. The resulting phase diagram in the temperature-chemical potential T − μ plane is in quite good agreement with the one from recent lattice results and effective models of QCD.
120206017
Heavy Quark Potential and QCD Beta Function from a Deformed AdS5 Model
We show that in a deformed ${\rm AdS}_5$ model with an explicit infrared cutoff included in the logarithmic correction $-c_0\log[(z_{IR}-z)/z_{IR}]$, the heavy quark Cornell potential can be fitted very well, the corresponding beta-function agrees with the QCD beta-function at 2-loop level reasonably well, and its dual dilaton potential is bounded from below in infrared. The results are compared with those in the Andreev-Zakharov model and the Pirner-Galow model.
119239121
Thermodynamics of deformed AdS5 model with a positive/negative quadratic correction in graviton-dilaton system
By solving the Einstein equations of the graviton coupling with a real scalar dilaton field, we establish a general framework to self-consistently solve the geometric background with black-hole for any given phenomenological holographic models. In this framework, we solve the black-hole background, the corresponding dilaon field and the dilaton potential for the deformed AdS5 model with a positive/negative quadratic correction. We systematically investigate the thermodynamical properties of the deformed AdS5 model with a positive and negative quadratic correction, respectively, and compare with lattice QCD on the results of the equation of state, the heavy quark potential, the Polyakov loop and the spatial Wilson loop. We find that the bulk thermodynamical properties are not sensitive to the sign of the quadratic correction, and the results of both deformed holographic QCD models agree well with lattice QCD result for pure SU(3) gauge theory. However, the results from loop operators favor a positive quadratic correction, which agree well with lattice QCD result. Especially, the result from the Polyakov loop excludes the model with a negative quadratic correction in the warp factor of AdS5.
117053356
On Holographic Entanglement Entropy with Second Order Excitations
Abstract We study the low-energy corrections to the holographic entanglement entropy (HEE) in the boundary CFT by perturbing the bulk geometry up to second order excitations. Focusing on the case that the boundary subsystem is a strip, we show that the area of the bulk minimal surface can be expanded in terms of the conserved charges, such as mass, angular momentum and electric charge of the AdS black brane. We also calculate the variation of the energy in the subsystem and verify the validity of the first law-like relation of thermodynamics at second order. Moreover, the HEE is naturally bounded at second order perturbations if the cosmic censorship conjecture for the dual black hole still holds.