Refined Counting of Necklaces in One-loop N=4\mathcal{N}=4 SYM

We compute the grand partition function of $\mathcal{N}=4$ SYM at one-loop in the $SU(2)$ sector with general chemical potentials, extending the results of P\'olya's theorem. We make use of finite group theory, applicable to all orders of $1/N_c$ expansion. We show that only the planar terms contribute to the grand partition function, which is therefore equal to the grand partition function of an ensemble of XXX$_\frac12$ spin chains. We discuss how Hagedorn temperature changes on the complex plane of chemical potentials.Comment: 34 pages, v2: typo corrected, v3: added a subsection about finite Nc, to appear in JHE

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

Transfer Characteristics in Graphene Field-Effect Transistors with Co Contacts

Graphene field-effect transistors with Co contacts as source and drain electrodes show anomalous distorted transfer characteristics. The anomaly appears only in short-channel devices (shorter than approximately 3 micrometers) and originates from a contact-induced effect. Band alteration of a graphene channel by the contacts is discussed as a possible mechanism for the anomalous characteristics observed.Comment: 10 pages, 3 figures, Appl. Phys. Let

Five-loop Konishi from the Mirror TBA

We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator. We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae. This constitutes an important test of the AdS/CFT TBA system.Comment: 14 pages, 2 figures, v2: published versio

Large Winding Sector of AdS/CFT

We study a family of classical strings on R x S^3 subspace of the AdS_5 x S^5 background that interpolates between pulsating strings and single-spike strings. They are obtained from the helical strings of hep-th/0609026 by interchanging worldsheet time and space coordinates, which maps rotating/spinning string states with large spins to oscillating states with large winding numbers. From a finite-gap perspective, this transformation is realised as an interchange of quasi-momentum and quasi-energy defined for the algebraic curve. The gauge theory duals are also discussed, and are identified with operators in the non-holomorphic sector of N=4 super Yang-Mills. They can be viewed as excited states above the ``antiferromagnetic'' state, which is ``the farthest from BPS'' in the spin-chain spectrum. Furthermore, we investigate helical strings on AdS_3 x S^1 in an appendix.Comment: 1+52 pages, 10 figures, v2: references and comments added, v3: minor changes and a reference adde