arXiv subjects

Song He

Publications and source records attributed to Song He.

At least 199 records · Page 11Linked to original sources

arXiv2016

String-inspired BCJ numerators for one-loop MHV amplitudes

We find simple expressions for the kinematic numerators of one-loop MHV amplitudes in maximally supersymmetric Yang-Mills theory and supergravity, for any multiplicity. The gauge theory numerators satisfy the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics, so that the gravity numerators are simply the square of the gauge theory ones. The duality holds because the numerators can be written in terms of structure constants of a kinematic algebra, which is familiar from the BCJ organization of self-dual gauge theory and gravity. The close connection that we find between one-loop amplitudes in the self-dual case and in the maximally supersymmetric case is the converse to the dimension-shifting formula. The starting point for arriving at our expressions is the dimensional reduction of ten-dimensional amplitudes obtained in the field-theory limit of open superstrings.

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arXiv2015

Chiral and Deconfining Phase Transitions from Holographic QCD Study

A first attempt to accommodate the chiral and deconfining phase transitions of QCD in the bottom-up holographic framework is given. We constrain the relation between dilaton field $ϕ$ and metric warp factor $A_e$ and get several reasonable models in the Einstein-Dilaton system. Using the potential reconstruction approach, we solve the corresponding gravity background. Then we fit the background-related parameters by comparing the equation of state with the two-flavor lattice QCD results. After that we study the temperature dependent behavior of Polyakov loop and chiral condensate under those background solutions. We find that the results are in good agreement with the two-flavor lattice results. All the studies about the equation of state, the Polyakov loop and the chiral condensate signal crossover behavior of the phase transitions, which is consistent with the current understanding on the QCD phase transitions with physical quark mass. Furthermore, the extracted transition temperatures are comparable with the two-flavor lattice QCD results.

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arXiv2015

The Amplituhedron and the One-loop Grassmannian Measure

All-loop planar scattering amplitudes in maximally supersymmetric Yang-Mills theory can be formulated geometrically in terms of the "amplituhedron". We study the mathematical structures of the one-loop amplituhedron, and present a new formula for its canonical measure, or the one-loop Grassmannian measure formula. Using the recently proposed momentum-twistor diagrams, we show that there is a correspondence between the cells of one-loop amplituhedron, BCFW terms or equivalently on-shell diagrams, and residues of the one-loop Grassmannian formula. In particular, for the first non-trivial case of one-loop NMHV, these structures are naturally associated with a nice geometric picture as polygons in projective space, as we discuss in various illustrative examples.

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arXiv2015

One-loop Scattering Equations and Amplitudes from Forward Limit

We show that the forward limit of tree-level scattering equations with two massive particles yields the SL(2,C)-covariant form of the one-loop scattering equations recently proposed by Geyer et al. We clarify several properties about these equations and the formulas at one loop. We then argue that in the bi-adjoint scalar theory, such forward limit yields the correct one-loop massless amplitudes, which leads to a new formula for the latter.

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arXiv2015

Entanglement Entropy for Descendent Local Operators in 2D CFTs

We mainly study the Rényi entropy and entanglement entropy of the states locally excited by the descendent operators in two dimensional conformal field theories (CFTs). In rational CFTs, we prove that the increase of entanglement entropy and Rényi entropy for a class of descendent operators, which are generated by $\cal{L}^{(-)}\bar{\cal{L}}^{(-)}$ onto the primary operator, always coincide with the logarithmic of quantum dimension of the corresponding primary operator. That means the Rényi entropy and entanglement entropy for these descendent operators are the same as the ones of their corresponding primary operator. For 2D rational CFTs with a boundary, we confirm that the Rényi entropy always coincides with the logarithmic of quantum dimension of the primary operator during some periods of the evolution. Furthermore, we consider more general descendent operators generated by $\sum_{} d_{\{n_i\}\{n_j\}}(\prod_{i} L_{-n_i}\prod_{j}{\bar L}_{-n_j})$ on the primary operator. For these operators, the entanglement entropy and Rényi entropy get additional corrections, as the mixing of holomorphic and anti-holomorphic Virasoro generators enhance the entanglement. Finally, we employ perturbative CFT techniques to evaluate the Rényi entropy of the excited operators in deformed CFT. The Rényi and entanglement entropies are increased, and get contributions not only from local excited operators but also from global deformation of the theory.

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arXiv2015

Rényi entropy of locally excited states with thermal and boundary effect in 2D CFTs

We 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 evolution of Rényi entropy does not depend on the choice of boundary conditions and boundary will change the time evolution of Rényi entropy. Moreover, in 2D rational CFTs with a boundary, we show that the Rényi entropy always coincides with the log of quantum dimension of the primary operator during some periods of the evolution. We make use of a quasi-particle picture to understand this phenomenon. In terms of quasi-particle interpretation, the boundary behaves as an infinite potential barrier which reflects any energy moving towards the boundary.

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arXiv2015

New Double Soft Emission Theorems

We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, DBI, Einstein-Maxwell-Scalar, NLSM and Yang-Mills-Scalar. We use the recently found CHY representation of these theories in order to give a simple proof of the leading order part of all these theorems

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arXiv2015

Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM

The 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 $ϕ^4$ 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.

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arXiv2015

Notes on Entanglement Entropy in String Theory

In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on the Rindler space. This entropy is also called the conical entropy and includes surface term contributions. We first derive a new simple formula of the conical entropy for any free higher spin fields. Then we apply this formula to computations of conical entropy in open and closed superstring. In our analysis of closed string, we study the twisted conical entropy defined by making use of string theory on Melvin backgrounds. This quantity is easier to calculate owing to the folding trick. Our analysis shows that the entanglement entropy in closed superstring is UV finite owing to the string scale cutoff.

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arXiv2014

Temperature dependent transport coefficients in a dynamical holographic QCD model

We investigate temperature dependent behavior of various transport coefficients in a dynamical holographical QCD model. We show the nontrivial temperature dependent behavior of the transport coefficients, like bulk viscosity, electric conductivity as well as jet quenching parameter, and it is found that all these quantities reveal information of the phase transition. Furthermore, with introducing higher derivative corrections in 5D gravity, the shear viscosity over entropy density ratio also shows a valley around phase transition, and it is found that the shear viscosity over entropy density ratio times the jet quenching over temperature cubic ratio almost remains as a constant above phase transition, and the value is two times larger than the perturbative result in Phys.Rev.Lett.99.192301(2007).

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arXiv2014

Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations

We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of $n$ massless particles are given by integrals over the positions of $n$ points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein--Yang--Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke--Taylor-like factors of subsets of particle labels.

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arXiv2014

The Amplituhedron from Momentum Twistor Diagrams

We propose a new diagrammatic formulation of the all-loop scattering amplitudes/Wilson loops in planar N=4 SYM, dubbed the "momentum-twistor diagrams". These are on-shell-diagrams obtained by gluing trivalent black and white vertices defined 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 for the latter we identify an isolated bubble-structure for each loop variable, arising from a forward limit, or entangled removal of particles. From a given diagram one can directly read off the C, D matrices via a generalized "boundary measurement"; this in turn determines a cell in the amplituhedron associated with the amplitude, and our diagrammatic representations of the amplitude can provide triangulations of the amplituhedron with generally very intricate geometries. To demonstrate the computational power of the formalism, we give explicit results for general two-loop integrands, and the cells of the complete amplituhedron for two-loop MHV amplitudes.

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arXiv2014

More on Soft Theorems: Trees, Loops and Strings

We study soft theorems in a broader context, addressing their fate at loop level and their universality in effective field theories and string theory. We argue that for gauge theories in the planar limit, loop-level soft gluon theorems can be made manifest already at the integrand level. In particular, we show that the planar integrand for N=4 SYM satisfies the tree-level soft theorem to all orders in perturbation theory and provide strong evidence to this effect for integrands in N<4 SYM. We consider soft theorems for non-supersymmetric Yang-Mills theories and gravity, and show the validity of integrand soft theorem, while loop corrections to the integrated soft theorems are intimately tied to the presence of conformal anomalies. We then address the question of universality of the soft theorems for various theories. In effective field theories with F^3 and R^3 interactions, the soft theorems are not modified. However for gravity theories with R^2 phi interactions, the sub-sub-leading order soft graviton theorem, which is beyond what is implied by the extended BMS symmetry, requires modifications at tree level for non-supersymmetric theories, and at loop level for N<5 supergravity due to anomalies. Finally, for superstring amplitudes at finite alpha', via explicit calculation for lower-point examples as well as world-sheet OPE analysis for arbitrary multiplicity, we show that the superstring amplitudes satisfy the same soft theorem as its field-theory counterpart. This is no longer true for bosonic closed strings due to the presence of R^2 phi interactions.

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arXiv2014

Loop Corrections to Soft Theorems in Gauge Theories and Gravity

In this paper, we study loop corrections to the recently proposed new soft theorem of Cachazo-Strominger, for both gravity and gauge theory amplitudes. We first review the proof of its tree-level validity based on BCFW recursion relations, which also establishes an infinite series of universals soft functions for MHV amplitudes, and a generalization to supersymmetric cases. For loop corrections, we focus on infrared finite, rational amplitudes at one loop, and apply recursion relations with boundary or double-pole contributions. For all-plus amplitudes, we prove that the subleading soft-theorems are exact to all multiplicities for both gauge and gravity amplitudes. For single-minus amplitudes, while the subleading soft-theorems are again exact for the minus-helicity soft leg, for plus-helicity loop corrections are required. Using recursion relations, we identify the source of such mismatch as stemming from the special contribution containing double poles, and obtain the all-multiplicity one-loop corrections to the subleading soft behavior in Yang-Mills theory. We also comment on the derivation of soft theorems using BCFW recursion in arbitrary dimensions.

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arXiv2014

Quantum Dimension as Entanglement Entropy in 2D CFTs

We study entanglement entropy of excited states in two dimensional conformal field theories (CFTs). Especially we consider excited states obtained by acting primary operators on a vacuum. We show that under its time evolution, entanglement entropy increases by a finite constant when the causality condition is satisfied. Moreover, in rational CFTs, we prove that this increased amount of (both Renyi and von-Neumann) entanglement entropy always coincides with the log of quantum dimension of the primary operator.

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arXiv2013

A Holographic Study on Vector Condensate Induced by a Magnetic Field

We study a holographic model with vector condensate by coupling the anti-de Sitter gravity to an Abelian gauge field and a charged vector field in $(3+1)$ dimensional spacetime. In this model there exists a non-minimal coupling of the vector filed to the gauge field. We find that there is a critical temperature below which the charged vector condenses via a second order phase transition. The DC conductivity becomes infinite and the AC conductivity develops a gap in the condensed phase. We study the effect of a background magnetic field on the system. It is found that the background magnetic field can induce the condensate of the vector field even in the case without chemical potential/charge density. In the case with non-vanishing charge density, the transition temperature raises with the applied magnetic field, and the condensate of the charged vector operator forms a vortex lattice structure in the spatial directions perpendicular to the magnetic field.

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arXiv2013

Entanglement Temperature in Non-conformal Cases

Potential reconstruction can be used to find various analytical asymptotical AdS solutions in Einstein dilation system generally. We have generated two simple solutions without physical singularity called zero temperature solutions. We also proposed a numerical way to obtain black hole solution in Einstein dilaton system with special dilaton potential. By using this method, we obtain the corresponding black hole solutions numerically and investigate the thermal stability of the black hole by comparing the free energy of thermal gas and the corresponding black hole. In two groups of non-conformal gravity solutions obtained in this paper, we find that the two thermal gas solutions are more unstable than black hole solutions respectively. Finally, we consider black hole solutions as a thermal state of zero temperature solutions to check that the first thermal dynamical law exists in entanglement system from holographic point of view.

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arXiv2013

Scattering of Massless Particles: Scalars, Gluons and Gravitons

In a recent note we presented a compact formula for the complete tree-level S-matrix of pure Yang-Mills and gravity theories in arbitrary spacetime dimension. In this paper we show that a natural formulation also exists for a massless colored cubic scalar theory. In Yang-Mills, the formula is an integral over the space of n marked points on a sphere and has as integrand two factors. The first factor is a combination of Parke-Taylor-like terms dressed with U(N) color structures while the second is a Pfaffian. The S-matrix of a U(N)xU(N') cubic scalar theory is obtained by simply replacing the Pfaffian with a U(N') version of the previous U(N) factor. Given that gravity amplitudes are obtained by replacing the U(N) factor in Yang-Mills by a second Pfaffian, we are led to a natural color-kinematics correspondence. An expansion of the integrand of the scalar theory leads to sums over trivalent graphs and are directly related to the KLT matrix. We find a connection to the BCJ color-kinematics duality as well as a new proof of the BCJ doubling property that gives rise to gravity amplitudes. We end by considering a special kinematic point where the partial amplitude simply counts the number of color-ordered planar trivalent trees, which equals a Catalan number. The scattering equations simplify dramatically and are equivalent to a special Y-system with solutions related to roots of Chebyshev polynomials.

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