Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra

We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a signle complex matrix. We also discuss the matrix quantum mechanics relevant to N=4 SYM on S^{3} times R. A commuting set of conserved operators whose eigenstates are given by the orthogonal basis is shown by using enhanced symmetries at zero coupling.Comment: 29 pages, typos corrected, references adde

Atomic masses of intermediate-mass neutron-deficient nuclei with relative uncertainty down to 35-ppb via multireflection time-of-flight mass spectrograph

High-precision mass measurements of $^{63}$Cu, $^{64-66}$Zn, $^{65}$Ga, $^{65-67}$Ge, $^{67}$As, $^{78,81}$Br, $^{80}$Rb, and $^{79}$Sr were performed utilizing a multireflection time-of-flight mass spectrograph combined with the gas-filled recoil ion separator GARIS-II. In the case of $^{65}$Ga, a mass uncertainty of 2.1 keV, corresponding to a relative precision of $\delta m / m = 3.5\times10^{-8}$, was obtained and the mass value is in excellent agreement with the 2016 Atomic Mass Evaluation. For $^{67}$Ge and $^{81}$Br, where masses were previously deduced through indirect measurements, discrepancies with literature values were found. The feasibility of using this device for mass measurements of nuclides more neutron-deficient side, which have significant impact on the $rp$-process pathway, is discussed.Comment: 15 pages, 6 figures, 1 tabl

Beyond the Planar Limit in ABJM

In this article we consider gauge theories with a U(N)X U(N) gauge group. We provide, for the first time, a complete set of operators built from scalar fields that are in the bi fundamental of the two groups. Our operators diagonalize the two point function of the free field theory at all orders in 1/N. We then use this basis to investigate non-planar anomalous dimensions in the ABJM theory. We show that the dilatation operator reduces to a set of decoupled harmonic oscillators, signaling integrability in a nonplanar large N limit.Comment: v2: minor revisison

Surprisingly Simple Spectra

The large N limit of the anomalous dimensions of operators in ${\cal N}=4$ super Yang-Mills theory described by restricted Schur polynomials, are studied. We focus on operators labeled by Young diagrams that have two columns (both long) so that the classical dimension of these operators is O(N). At large N these two column operators mix with each other but are decoupled from operators with $n\ne 2$ columns. The planar approximation does not capture the large N dynamics. For operators built with 2, 3 or 4 impurities the dilatation operator is explicitly evaluated. In all three cases, in a certain limit, the dilatation operator is a lattice version of a second derivative, with the lattice emerging from the Young diagram itself. The one loop dilatation operator is diagonalized numerically. All eigenvalues are an integer multiple of $8g_{YM}^2$ and there are interesting degeneracies in the spectrum. The spectrum we obtain for the one loop anomalous dimension operator is reproduced by a collection of harmonic oscillators. This equivalence to harmonic oscillators generalizes giant graviton results known for the BPS sector and further implies that the Hamiltonian defined by the one loop large $N$ dilatation operator is integrable. This is an example of an integrable dilatation operator, obtained by summing both planar and non-planar diagrams.Comment: 34 page

Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality

We propose gauge theory operators built using a complex Matrix scalar which are dual to brane-anti-brane systems in $AdS_5 \times S^5$, in the zero coupling limit of the dual Yang-Mills. The branes involved are half-BPS giant gravitons. The proposed operators dual to giant-anti-giant configurations satisfy the appropriate orthogonality properties. Projection operators in Brauer algebras are used to construct the relevant multi-trace Matrix operators. These are related to the ``coupled representations'' which appear in 2D Yang-Mills theory. We discuss the implications of these results for the quantum mechanics of a complex matrix model, the counting of non-supersymmetric operators and the physics of brane-anti-brane systems. The stringy exclusion principle known from the properties of half-BPS giant gravitons, has a new incarnation in this context. It involves a qualitative change in the map between brane-anti-brane states to gauge theory operators. In the case of a pair of sphere giant and anti-giant this change occurs when the sum of the magnitudes of their angular momenta reaches $N$.Comment: 52 pages, 10 figure

On the Open-Closed B-Model

We study the coupling of the closed string to the open string in the topological B-model. These couplings can be viewed as gauge invariant observables in the open string field theory, or as deformations of the differential graded algebra describing the OSFT. This is interpreted as an intertwining map from the closed string sector to the deformation (Hochschild) complex of the open string algebra. By an explicit calculation we show that this map induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Reversely, this can be used to derive the closed string from the open string. We shortly comment on generalizations to other models, such as the A-model.Comment: LaTeX, 48 pages. Citation adde

Magnetic Properties in Non-centrosymmetric Superconductors with and without Antiferromagnetic Order

The paramagnetic properties in non-centrosymmetric superconductors with and without antiferromagnetic (AFM) order are investigated with focus on the heavy Fermion superconductors, CePt_3Si, CeRhSi_3 and CeIrSi_3. First, we investigate the spin susceptibility in the linear response regime and elucidate the role of AFM order. The spin susceptibility at T=0 is independent of the pairing symmetry and increases in the AFM state. Second, the non-linear response to the magnetic field are investigated on the basis of an effective model for CePt_3Si which may be also applicable to CeRhSi_3 and CeIrSi_3. The role of antisymmetric spin-orbit coupling (ASOC), helical superconductivity, anisotropic Fermi surfaces and AFM order are examined in the dominantly s-, p- and d-wave states. We emphasize the qualitatively important role of the mixing of superconducting (SC) order parameters in the p-wave state which enhances the spin susceptibility and suppresses paramagnetic depairing effect in a significant way. Therefore, the dominantly p-wave superconductivity admixed with the s-wave order parameter is consistent with the paramagnetic properties of CePt_3Si at ambient pressure. We propose some experiments which can elucidate the novel pairing states in CePt_3Si as well as CeRhSi_3 and CeIrSi_3.Comment: To appear in J. Phys. Soc. Jpn. (2007) No.1

Anomalous Spin Response in Non-centrosymmetric Compounds

We examine static spin susceptibilities $\chi_{\alpha\beta}({\bf q})$ of spin components $S_{\alpha}$ and $S_{\beta}$ in the non-centrosymmetric tetragonal system. These show anomalous momentum dependences like $\chi_{xx}({\bf q})-\chi_{yy}({\bf q})\sim q_x^2-q_y^2$ and $\chi_{xy}({\bf q})+\chi_{yx}({\bf q})\sim q_x q_y$, which vanish in centrosymmetric systems. The magnitudes of the anomalous spin susceptibilities are enhanced by the on-site Coulomb interaction, especially, around an ordering wave vector. The significant and anomalous momentum dependences of these susceptibilities are explained by a group theoretical analysis. As the direct probe of the anomalous spin susceptibility, we propose a polarized neutron scattering experiment.Comment: 4 pages, 1 table, 4 figure

Nonplanar integrability at two loops

In this article we compute the action of the two loop dilatation operator on restricted Schur polynomials that belong to the su(2) sector, in the displaced corners approximation. In this non-planar large N limit, operators that diagonalize the one loop dilatation operator are not corrected at two loops. The resulting spectrum of anomalous dimensions is related to a set of decoupled harmonic oscillators, indicating integrability in this sector of the theory at two loops. The anomalous dimensions are a non-trivial function of the 't Hooft coupling, with a spectrum that is continuous and starting at zero at large N, but discrete at finite N.Comment: version to appear in JHE