arXiv subjects

Gaoli Chen

Publications and source records attributed to Gaoli Chen.

6 recordsLinked to original sources

arXiv2019

Structure constants of heavy operators in ABJM/ABJ Theory

Efficient and powerful approaches to the computation of correlation functions involving determinant, sub-determinant and permanent operators, as well as traces, have recently been developed in the setting of ${\cal N}=4$ super Yang-Mills theory. In this article we show that they can be extended to ABJM and ABJ theory. After making use of a novel identity which follows from character orthogonality, an integral representation of certain projection operators used to define Schur polynomials is given. This integral representation provides an effective description of the correlation functions of interest. The resulting effective descriptions have ${1\over N}$ as the loop counting parameter, strongly suggesting their relevance for holography.

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arXiv2019

Absorption of closed strings by giant gravitons

A new approach to the computation of correlation functions involving two determinant operators as well as one non-protected single trace operator has recently been developed by Jiang, Komatsu and Vescovi. This correlation function provides the holographic description of the absorption of a closed string by a giant graviton. The analysis has a natural interpretation in the framework of group representation theory, which admits a generalization to general Schur polynomials and restricted Schur polynomials. This generalizes the holographic description to any giant or dual giant gravitons which carry more than one angular momentum on the sphere. For a restricted Schur polynomial labeled by a column with $N$ boxes (dual to a maximal giant graviton) we find evidence in favor of integrability.

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arXiv2018

Cubic Interaction Vertices and One-loop Self-energy in the Stable String Bit Model

We provide a formalism to calculate the cubic interaction vertices of the stable string bit model, in which string bits have $s$ spin degrees of freedom but no space to move. With the vertices, we obtain a formula for one-loop self-energy, i.e., the $\mathcal{O}\left(1/N^{2}\right)$ correction to the energy spectrum. A rough analysis shows that, when the bit number $M$ is large, the ground state one-loop self-energy $ΔE_{G}$ scale as $M^{5-s/4}$ for even $s$ and $M^{4-s/4}$ for odd $s$. Particularly, in $s=24$, we have $ΔE_{G}\sim 1/M$, which resembles the Poincaré invariant relation $P^{-}\sim 1/P^{+}$ in $(1+1)$ dimensions. We calculate analytically the one-loop correction for the ground energies with $M=3$ and $s=1,\,2$. We then numerically confirm that the large $M$ behavior holds for $s\leq4$ cases.

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arXiv2018

Clebsch-Gordan coefficients of discrete groups in subgroup bases

We express each Clebsch-Gordan (CG) coefficient of a discrete group as a product of a CG coefficient of its subgroup and a factor, which we call an embedding factor. With an appropriate definition, such factors are fixed up to phase ambiguities. Particularly, they are invariant under basis transformations of irreducible representations of both the group and its subgroup. We then impose on the embedding factors constraints, which relate them to their counterparts under complex conjugate and therefore restrict the phases of embedding factors. In some cases, the phase ambiguities are reduced to sign ambiguities. We describe the procedure of obtaining embedding factors and then calculate CG coefficients of the group \mathcal{PSL}_{2}\left(7\right) in terms of embedding factors of its subgroups S_{4} and \mathcal{T}_{7}.

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arXiv2016

Numerical Study of the Simplest String Bit Model

String bit models provide a possible method to formulate a string as a discrete chain of pointlike string bits. When the bit number $M$ is large, a chain behaves as a continuous string. We study the simplest case that has only one bosonic bit and one fermionic bit. The creation and annihilation operators are adjoint representations of the $U\left(N\right)$ color group. We show that the supersymmetry reduces the parameter number of a Hamiltonian from 7 to 3 and, at $N=\infty$, ensures a continuous energy spectrum, which implies the emergence of one spatial dimension. The Hamiltonian $H_{0}$ is constructed so that in the large $N$ limit it produces a world sheet spectrum with one Grassmann world sheet field. We concentrate on numerical study of the model in finite $N$. For the Hamiltonian $H_{0}$, we find that the would-be ground energy states disappear at $N=\left(M-1\right)/2$ for odd $M\leq11$. Such a simple pattern is spoiled if $H$ has an additional term $ξΔH$ which does not affect the result of $N=\infty$. The disappearance point moves to higher (lower) $N$ when $ξ$ increases (decreases). Particularly, the $\pm\left(H_{0}-ΔH\right)$ cases suggest a possibility that the ground state could survive at large $M$ and $M\gg N$. Our study reveals that the model has stringy behavior: when $N$ is fixed and large enough, the ground energy decreases linearly with respect to $M$, and the excitation energy is roughly of order $M^{-1}$. We also verify that a stable system of Hamiltonian $\pm H_{0}+ξΔH$ requires $ξ\geq\mp1$.

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arXiv2015

Neutrino masses, the $μ$-term and $\mathcal{ PSL}_2(7)$

Using an $SO(10)$-inspired form for the Dirac neutrino mass, we map the neutrino data to right-handed neutrino Majorana mass-matrix, $\mathcal M$, and investigate a special form with \emph{seesaw} tribimaximal mixing; it predicts a normal hierarchy, and the values of the light neutrino masses. It may be generated by mapping the top quark hierarchy onto the vacuum values of familon fields transforming under the family group $\mathcal{ PSL}_2(7)$. We next investigate the hypothesis that these familons play a dual role, generating a hierarchy in the supersymmetric $\mathbf μ$-mass matrix of Higgses carrying family quantum numbers. A special $\mathcal{ PSL}_2(7)$ invariant coupling produces a $μ$-matrix with a hierarchy of thirteen orders of magnitude. Only one Higgs field (per hypercharge sector) is light enough (with a $μ$-mass $\sim 10-100$ GeV) to be destabilized by SUSY soft breaking at the TeV scale, and upon spontaneous symmetry breaking, gives \emph{tree-level} masses for the heaviest family.

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