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

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

Hedging Diffusion Processes by Local Risk-Minimisation with Applications to Index Tracking

The solution to the problem of hedging contingent claims by local risk-minimisation has been considered in detail in Follmer and Sondermann (1986), Follmer and Schweizer (1991) and Schweizer (1991). However, given a stochastic process Xt and tau1 tau2, the strategy that is locally risk-minimising for Xtau1 is in general not locally risk-minimising for Xtau2. In the case of diffusion processes, this paper considers the problem of determining a strategy that is simultaneously locally risk-minimising for Xtau for all tau. That is, a strategy that is locally risk-minimising for the entire process Xt. The necessary and sufficient conditions under which this is possible are obtained, and applied to the problem of index tracking. In particular, a close connection between the local risk-minimising and the tracking error variance minimising strategies for index tracking is established, and leads to a simple criterion for the selection of optimal set of assets from which to form a tracker portfolio, as well as a value-at-risk type measure for the set of assets used.minimal martingale measure; local risk-minimisation; hedging; incomplete market; index tracking; portfolio selection

N=3{\cal N}=3 Supersymmetric Effective Action of D2-branes in Massive IIA String Theory

We obtain a new-type of ${\cal N}=3$ Yang-Mills Chern-Simons theory from the Mukhi-Papageorgakis Higgsing of the ${\cal N}=3$ Gaiotto-Tomasiello theory. This theory has ${\cal N}=1$ BPS fuzzy funnel solution which is expressed in terms of the seven generators of SU(3), excluding $T_8$. We propose that this is an effective theory of multiple D2-branes with D6- and D8-branes background in massive IIA string theory.Comment: 22 pages, positive definite form of potential is added, some comments are change

Structure of Stochastic Dynamics near Fixed Points

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition, but might have instead a divergence-free probability current. In the linear case the force can be split into two parts, one of which gives detailed balance with the diffusive motion, while the other induces cyclic motion on surfaces of constant cost function. Using the Jordan transformation for the force matrix, we find an explicit construction of the cost function. We discuss singularities of the transformation and their consequences for the stationary distribution. This Boltzmann-like distribution may be not unique, and nonlinear effects and boundary conditions may change the distribution and induce additional currents even in the neighborhood of a fixed point.Comment: 7 page

Thermal activation energy of 3D vortex matter in NaFe1-xCoxAs (x=0.01, 0.03 and 0.07) single crystals

We report on the thermally activated flux flow dependency on the doping dependent mixed state in NaFe1-xCoxAs (x=0.01, 0.03, and 0.07) crystals using the magnetoresistivity in the case of B//c-axis and B//ab-plane. It was found clearly that irrespective of the doping ratio, magnetoresistivity showed a distinct tail just above the Tc, offset associated with the thermally activated flux flow (TAFF) in our crystals. Furthermore, in TAFF region the temperature dependence of the activation energy follows the relation U(T, B)=U_0 (B) (1-T/T_c )^q with q=1.5 in all studied crystals. The magnetic field dependence of the activation energy follows a power law of U_0 (B)~B^(-{\alpha}) where the exponent {\alpha} is changed from a low value to a high value at a crossover field of B=~2T, indicating the transition from collective to plastic pinning in the crystals. Finally, it is suggested that the 3D vortex phase is the dominant phase in the low-temperature region as compared to the TAFF region in our series samples

Evaluating the Diversity of Emergency Medicine Foundation (EMF) Grant Recipients in the Last Decade

On behalf of the ACEP Research CommitteeIntroduction: To study diversity of researchers and barriers to success among Emergency Medicine Foundation (EMF) grant recipients in the last 10 years.Methods: EMF grant awardees were approached to complete a brief survey, which included demographics, queries related to contributions to the literature, success in obtaining grants, and any perceived barriers they encountered.Results: Of the 342 researchers contacted by email, a total of 147 completed the survey for a response rate of 43%. The respondents were predominately mid to late career white-male-heterosexual-Christian with an average age of 44 years (range 25-69 years of age). With regards to training and education, the majority of respondents (50%) were either Associate or Professor clinical rank (8% instructor/resident/fellow and 31% Assistant). Sixty-two percent of the respondents reported perceived barriers to career advancement since completion of residency. The largest perceived barrier to success was medical specialty (26%), followed by gender (21%) and age (16%).Conclusion: Our survey of EMF grant recipients in the last 10 years shows a considerable lack of diversity. The most commonly perceived barriers to career advancement by this cohort were medical specialty, gender, and age. An opportunity exists for further definition of barriers and development of mechanisms to overcome them, with a goal of increased success for those that are underrepresented.