Abelian Gauge Invariance of the WZ-type Coupling in ABJM Theory

We construct the interaction terms between the worldvolume fields of multiple M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context of ABJM theory. The obtained Wess-Zumino-type coupling is simultaneously invariant under the U$_{\textrm{L}}(N)\times$U$_{\textrm{R}}(N)$ non-Abelian gauge transformation of the ABJM theory and the Abelian gauge transformation of the 3-form field in 11-dimensional supergravity.Comment: 16 pages, minor corrections, published versio

Gravity from Entanglement and RG Flow in a Top-down Approach

The duality between a $d$-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS$_{d+1}$ geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS$_4$ gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS$_4$ metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.Comment: 42 pages, no figure, minor corrections, references adde

Exact Holography of the Mass-deformed M2-brane Theory

We test the holographic relation between the vacuum expectation values of gauge invariant operators in ${\cal N} = 6$ ${\rm U}_k(N)\times {\rm U}_{-k}(N)$ mass-deformed ABJM theory and the LLM geometries with $\mathbb{Z}_k$ orbifold in 11-dimensional supergravity. To do that, we apply the Kaluza-Klein reduction to construct a 4-dimensional gravity theory and implement the holographic renormalization procedure. We obtain an exact holographic relation for the vacuum expectation values of the chiral primary operator with conformal dimension $\Delta = 1$, which is given by $\langle {\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)}$, for large $N$ and $k=1$. Here factor $f_{(\Delta)}$ is independent of $N$. Our results involve infinite number of exact dual relations for all possible supersymmetric Higgs vacua and so provide a nontrivial test of gauge/gravity duality away from the conformal fixed point. We also extend our results to the case of $k\ne 1$ for LLM geometries represented by rectangular-shaped Young-diagrams.Comment: 6 pages, major corrections in section 3 and 4, references added, title change

Effective Potential Theory: A Practical Way to Extend Plasma Transport Theory to Strong Coupling

The effective potential theory is a physically motivated method for extending traditional plasma transport theories to stronger coupling. It is practical in the sense that it is easily incorporated within the framework of the Chapman-Enskog or Grad methods that are commonly applied in plasma physics and it is computationally efficient to evaluate. The extension is to treat binary scatterers as interacting through the potential of mean force, rather than the bare Coulomb or Debye-screened Coulomb potential. This allows for aspects of many-body correlations to be included in the transport coefficients. Recent work has shown that this method accurately extends plasma theory to orders of magnitude stronger coupling when applied to the classical one-component plasma model. The present work shows that similar accuracy is realized for the Yukawa one-component plasma model and it provides a comparison with other approaches.Comment: 6 pages, 3 figures, Proceedings of the Strongly Coupled Coulomb Systems conference 201

Mass-deformed ABJM Theory and LLM Geometries: Exact Holography

We present a detailed account and extension of our claim in arXiv:1610.01490. We test the gauge/gravity duality between the ${\cal N} = 6$ mass-deformed ABJM theory with U$_k(N)\times$U$_{-k}(N)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)/${\mathbb Z}_k$ $\times$SO(4)/${\mathbb Z}_k$ isometry, in the large $N$ limit. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein holography to the LLM geometries. We focus on the chiral primary operator with conformal dimension $\Delta = 1$. We show that $\langle {\cal O}^{(\Delta=1)}\rangle= N^{\frac32} \, f_{(\Delta=1)}$ for all supersymmetric vacuum solutions and LLM geometries with $k=1$, where the factor $f_{(\Delta)}$ is independent of $N$. We also confirm that the vacuum expectation value of the the energy momentum tensor is vanishing as expected by the supersymmetry. We extend our results to the case of $k\ne 1$ for LLM geometries represented by rectangular-shaped Young-diagrams. In analogy with the Coulomb branch of the ${\cal N} = 4$ super Yang-Mills theory, we argue that the discrete Higgs vacua of the mABJM theory as well as the corresponding LLM geometries are parametrized by the vevs of the chiral primary operators.Comment: 44 pages, 1 figure, major corrections in section 3 and 5, references added, title change

Inclusive angular distribution of alpha and Li fragments produced in the Fe-C and Fe-Pb collisions at 1.88 GeV/u

The LS (laboratory system) emission angles theta for 2188 and 298 Li fragments, produced inclusively in relativistic Fe-C and Fe-Pb collisions, have been measured in reference to incident Fe-ion beam tracks nearby in nuclear emulsion. An empirical differential frequency formula, dN(cot theta) = exp (a + b cot theta)d(cot theta) is obtained with the constant b approx. = -0.026 at 1.88 GeV/u, which seems to be independent on the kinds of target nucleus as well as on the kinds of projectile fragments