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.
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.
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.
119290604
The amplituhedron from momentum twistor diagrams
A bstractWe propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N$$ \mathcal{N} $$ = 4 SYM, dubbed the “momentum-twistor diagrams”. These are on-shell-diagrams obtained by gluing trivalent black and white vertices in momentum twistor space, which, in the reduced diagram case, are known to be related to diagrams in the original twistor space. The new diagrams are manifestly Yangian invariant, and they naturally represent factorization and forward-limit contributions in the all-loop BCFW recursion relations in momentum twistor space, in a fashion that is completely different from those in momentum space. We show how to construct and evaluate momentum-twistor diagrams, and how to use them to obtain tree-level amplitudes and loop-level integrands; in particular the latter involve isolated bubble-structures for loop variables arising from forward limits, or the entangled removal of particles. From each diagram, the generalized “boundary measurement” directly gives the C, D matrices, thus a cell in the amplituhedron associated with the amplitude, and we expect that our diagrammatic representations of the amplitude provide triangulations of the amplituhedron. To demonstrate the computational power of the formalism, we give explicit results for general two-loop integrands, and the cells of the amplituhedron for two-loop MHV amplitudes.
119464468
Two Particle States in a Box and the $s$-Matrix in Multi-Channel Scattering
Using a quantum mechanical model, the exact energy eigenstates for two-particle two-channel scattering are studied in a cubic box with periodic boundary conditions. 
A relation between the exact energy eigenvalue in the box and the two-channel $S$-matrix elements in the continuum is obtained. This result can be viewed as a generalization of the well-known L\"uscher's formula which establishes a similar relation in elastic scattering.
5970885
Scattering of massless particles in arbitrary dimensions.
We present a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimensions. The new formula for the scattering of n particles is given by an integral over the positions of n points on a sphere restricted to satisfy a dimension-independent set of equations. The integrand is constructed using the reduced Pfaffian of a 2n×2n matrix, Ψ, that depends on momenta and polarization vectors. In its simplest form, the gravity integrand is a reduced determinant which is the square of the Pfaffian in the Yang-Mills integrand. Gauge invariance is completely manifest as it follows from a simple property of the Pfaffian.
118646566
Pseudoscalar glueball in a chiral Lagrangian model with instanton effect
We study the pseudoscalar glueball ground state in a chiral effective Lagrangian model proposed by 't Hooft, motivated by taking into account the instanton effects, which can describe not only the chiral symmetry breaking, but also the solution of U{sub A}(1). We study the parameter space allowed by constraints from vacuum conditions and unitary bounds. By considering two scenarios in the 0{sup ++} sector, we find that parameter space which can accommodate the 0{sup -+} sector is sensitive to the conditions in 0{sup ++} sector. From our analysis, it is found that three {eta} states, i.e. {eta}(1295), {eta}(1405), {eta}(1475), can be the pseudoscalar glueball ground state if we assume that the lightest 0{sup ++} glueball ground state has a mass 1710 (or 1500) MeV. While there will be no 0{sup -+} glueball candidate ground state found in experiments if we assume that the lightest 0{sup ++} glueball ground state has a mass 660 MeV. We also point out the determined instanton density (i.e. the parameter k{sub t}) is consistent with those determined from other methods, e.g. instanton liquid approximation and lattice simulations.
56229424
Phase structure in a dynamical soft-wall holographic QCD model
A bstractWe consider the Einstein-Maxwell-dilaton system with an arbitrary kinetic gauge function and a dilaton potential. A family of analytic solutions is obtained by the potential reconstruction method. We then study its holographic dual QCD model. The kinetic gauge function can be fixed by requesting the linear Regge spectrum of mesons. We calculate the free energy to obtain the phase diagram of the holographic QCD model and interpret our result as the heavy quarks system by comparing the recent lattice QCD simulation. We finally obtain the equations of state in our model.
121764215
Note on integrability of marginally deformed ABJ(M) theories
A bstractWe study the anomalous dimensions of operators in the scalar sector of β-deformed ABJ(M) theories. We show that the anomalous dimension matrix at two-loop order gives an integrable Hamiltonian acting on an alternating SU(4) spin chain with the spins at odd lattice sides in the fundamental representation and the spins at even lattices in the anti-fundamental representation. We get a set of β-deformed Bethe ansatz equations which give the eigenvalues of Hamiltonian of this deformed spin chain system. Based on our computations, we also extend our study to non-supersymmetric three-parameter γ-deformation of ABJ(M) theories and find that the corresponding Hamiltonian is the same as the one in β-deformed case at two-loop level in the scalar sector.
119971617
Quantum dimension as entanglement entropy in two dimensional conformal field theories
We study the entanglement entropy of excited states in two-dimensional conformal field theories (CFTs). In particular, we consider excited states obtained by acting on a vacuum with primary operators. We show that the entanglement entropy increases by a finite constant amount under its time evolution. Moreover, in rational conformal field theories, we prove that this increase of the (both Renyi and von Neumann) entanglement entropy always coincides with the log of the quantum dimension of the primary operator.
118493750
Massive superstring scatterings in the Regge regime
We calculate four classes of high-energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross regime can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidence that the existence of these four Gross regime ratios in the RR persists to subleading orders in the Regge expansion of all high-energy fermionic string scattering amplitudes.