Negative anomalous dimensions in N=4 SYM

We elucidate aspects of the one-loop anomalous dimension of $so(6)$-singlet multi-trace operators in $\mathcal{N}=4\ SU(N_c)$ SYM at finite $N_c$. First, we study how $1/N_c$ corrections lift the large $N_c$ degeneracy of the spectrum, which we call the operator submixing problem. We observe that all large $N_c$ zero modes acquire non-positive anomalous dimension starting at order $1/N_c^2$, and they mix only among the operators with the same number of traces at leading order. Second, we study the lowest one-loop dimension of operators of length equal to $2N_c$. The dimension of such operators becomes more negative as $N_c$ increases, which will eventually diverge in a double scaling limit. Third, we examine the structure of level-crossing at finite $N_c$ in view of unitarity. Finally we find out a correspondence between the large $N_c$ zero modes and completely symmetric polynomials of Mandelstam variables.Comment: 34+31 pages, many figures, a Mathematica file attached, v2: typos corrected, references added, section 5 revised, v3: revised Section 4 on correlators, and small detail

Mental health services and related factors in health care of traumatic brain injury survivors

Background: Family members can be confounded by cognitive and other changes that occur in traumatic brain injury (TBI) survivors, and feel burdened in providing their nursing care. Factors affecting mental health promotion in caregivers of patients with TBI-induced cognitive dysfunction have not been addressed fully. Objective: To maintain and improve mental health status of caregivers by clarifying the characteristics of TBI survivors and caregivers, and mental health status of caregivers. Methods: On a questionnaire survey, TBI survivors answered questions about their characteristics, activity of daily living, and symptoms of cognitive dysfunction, and caregivers answered questions about their characteristics and mental health status. We analyzed the impact of the individual levels of the items for TBI survivors and caregivers on the caregivers’ mental health status. Results: The mean General Health Questionnaire 30-item score was 14.8 ± 7.6 points, and mental illness was confirmed in 47 (75.8%) caregivers. The mental health status of the caregivers was more undermined when the nursing care period and sleep time of caregivers were short, when care was required for cosmetic preparation and dressing, and when the patient had symptoms of impaired executive dysfunction and social behavior

Magnetic properties of the spin-1/2 XXZ model on the Shastry-Sutherland lattice: Effect of long-range interactions

We study magnetic properties of the $S=1/2$ Ising-like XXZ model on the Shastry-Sutherland lattices with long-range interactions, using the quantum Monte Carlo method. This model shows magnetization plateau phases at one-half and one-third of the saturation magnetization when additional couplings are considered. We investigate the finite temperature transition to one-half and one-third plateau phases. The obtained results suggest that the former case is of the first order and the latter case is of the second order. We also find that the system undergoes two successive transitions with the 2D Ising model universality, although there is a single phase transition in the Ising limit case. Finally, we estimate the coupling ratio to explain the magnetization process observed in ${\rm TmB_4}$Comment: 5 pages, 6 figure

Energy-momentum tensor correlation function in Nf=2+1 full QCD at finite temperature

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in $N_f=2+1$ full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturbatively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing $=0.07$ fm. In this paper the temperature is limited to a single value $T=232$ MeV. The $u$, $d$ quark mass is rather heavy with $m_\pi/m_\rho=0.63$ while the $s$ quark mass is set to approximately its physical value.Comment: 9 pages, 4 figures. Talk presented at the 35th International Symposium on Lattice Field Theory (LATTICE 2017), 18-24 June 2017, Granada, Spai

Dimensional Reduction of the S3S^3/WZW Duality

Recently proposed duality relates the critical level limit $\hat{k} \to -2$ of $SU(2)_{\hat{k}}$ WZW models to a classical three-dimensional Einstein gravity on a sphere. In this paper, we propose a dimensional reduced version of this duality. The gravity side is reduced to a Jackiw-Teitelboim (JT) gravity on $S^2$ with a non-standard boundary term, or a BF theory with $SU(2)$ gauge symmetry. At least in low temperature limit, these two-dimensional gravity theories completely capture the original three-dimensional gravity effect. The CFT side is reduced to a certain complex Liouville quantum mechanics (LQM) with $SU(2)$ gauge symmetry. Our proposal gives an interesting example of a holography without boundary. We also discuss a higher-spin generalization with $SU(N)$ gauge symmetry.Comment: 36 page