Gabriel Catren, Laboratoire SPHERE, Université Paris Diderot - CNRS, Paris, France

On the Relation Between Gauge and Phase Symmetries

##### We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state (e.g. from q and p to q or p in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s moment map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture (proposed by Guillemin and Sternberg) according to which “quantization commutes with reduction”. In particular, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit (the extreme cases of) this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points.

Keitaro Nagata, KEK

Canonical approach to finite density QCD

##### Recently, QCD at finite temperature and density attracts renewed interests, stimulated by advances in lattice QCD technique for finite density system and a beam energy scan (BES) program, which is an on-going experiment at RHIC to investigate the QCD phase diagram.

Towards the understanding of QCD at finite density, we employ a canonical approach, which is based on a fundamental equation describing the relation between canonical and grand canonical partition functions. I will talk about its applications both to BES experiment and lattice QCD simulations.

First, we introduce the framework and explain possible applications, such as moments of the probability distribution and Lee-Yang zeros. Then, we apply the technique to data obtained in BES experiments. We show that the canonical approach enables us to investigate a wide range of QCD phase diagram using data obtained at a certain point (chemical freeze-out point).

Next, we study canonical partition functions and Lee-Yang zeros in lattice QCD simulations. They show a drastic change from the confinement to deconfinement phases. In addition, we analytically solve canonical partition functions and Lee-Yang zeros for high temperature QCD using a saddle point approximation. We find that the analytic result of Lee-Yang zeros explain a gross feature of those obtained from lattice QCD simulations. We discuss its implications to experimental data.

References

1. Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition

K. Nagata, K. Kashiwa, A. Nakamura, S. M. Nishigaki arXiv:1410.0783

2. Probing QCD Phase Structure by Baryon Multiplicity Distribution A. Nakamura, K. Nagata [arXiv:1305.0760]

3. Towards extremely dense matter on the lattice K. Nagata, S. Motoki, Y. Nakagawa, A. Nakamura, T.Saito [PTEP01A103(2012), arXiv:1204.1412]

Kazumi Kashiyama, University of California, Berkeley

Neutrino Tomography of GRB jet

##### The IceCube discovery of astrophysical sub-PeV neutrinos has opened a new era of multi-messenger astronomy. Relativistic GRB jets are a long-standing candidate source of such neutrinos, although no neutrino counterpart of the observed GRBs has been reported so far. Here, I overview possible neutrino production processes in GRB jet, and argue how far detections or even non-dentecions of such neutrino counterparts, combined with multi-band electromagnetic observations, can shape the physics of GRB jet in the next decade.

Dan Hooper, Fermi National Accelerator Laboratory

Dark matter Annihilation in the Galactic Center

##### Past studies have identified a spatially extended excess of ~1-3 GeV gamma rays from the region surrounding the Galactic Center, consistent with the emission expected from annihilating dark matter. Recent improvements in the analysis techniques have found this excess to be robust and highly statistically significant, with a spectrum, angular distribution, and overall normalization that is in good agreement with that predicted by simple annihilating dark matter models. For example, the signal is very well fit by a 31-40 GeV dark matter particle annihilating to b quarks with an annihilation cross section of sigma v = (1.7-2.3) x 10^-26 cm^3/s. Furthermore, the angular distribution of the excess is approximately spherically symmetric and centered around the dynamical center of the Milky Way (within ~0.05 degrees of Sgr A*), showing no sign of elongation along or perpendicular to the Galactic Plane. The signal is observed to extend to at least 10 degrees from the Galactic Center, disfavoring the possibility that this emission originates from millisecond pulsars.

Kantaro Ohmori, The Univ. of Tokyo

Anomaly polynomial of general 6d SCFTs

##### 6d N=(2,0) theories are the source of many beautiful stories on supersymmetric field theories whose dimensions are lower than six. We hope similar and richer stories hold for 6d N=(1,0) theories, although it should be much harder to investigate with fewer supersymmetries.

As a first step, we want better understanding of 6d theories and some calculable quantities of those theories. We found that the anomaly polynomials of 6d N=(2,0) or N=(1,0) SCFTs can be determined on their tensor branch using a kind of anomaly maching mechanism similar to the Green-Schwarz mechanism. Each self-dual tensor fields associated to tensor branch scalars can have non-trivial Bianchi identities, which results in contribution to the anomaly additional to contribution from naive 1-loop calculation. Anomaly matching conditions uniquely determines such contributions, enabling us to calculate anomaly polynomials.

In this talk, I will review 6d N=(1,0) SCFTs which can be constructed with branes of the M-thoery, and then talk about anomaly polynomials. Especially, I will focus on the world volume theories of M5-branes on the ALE-singularities of general type.

Tomoaki Ishiyama, Center for Computational Sciences, University of Tsukuba

Dark Matter Structure Formation Simulations on K Supercomputer

##### Smaller dark matter subhalos are more abundant in the Milky Way. The survivability of such subhalos in the Milky Way depends on their structure. This suggests that the structure of subhalos can determine the fine structure of the Milky Way halo. I report the results of high resolution cosmological simulations of very small scale structure formation peformed on K computer. I focus on the formation and evolution of dark matter halos near the free streaming scale, and their impact on the indirect dark matter detection experiments.

Guray Erkol, Ozyegin University

A look inside hadrons: What can we learn from theory?

##### One theoretical challenge in hadron physics is to understand the hadron structure and interactions from QCD. I will summarize some recent results as obtained from QCD, with special emphasis on the spin and electromagnetic structure of light and heavy hadrons. I will give a comparison of various approaches.

George Knee, NTT Basic Research Laboratories

Is weak-value amplification useful for metrology?

##### Weak value amplification is a technique combining both strong and weak quantum measurements which is gathering increased interest both theoretically and experimentally. The surprising effect arises when a weak measurement, where a quantum coherent measuring device is only weakly coupled to the system of interest, is followed by a strong measurement. Rarely, the measuring device can respond in an unusually energetic manner. I will discuss some approaches in statistical estimation theory, which may help to decide whether this effect can be exploited to increase the performance of quantum sensors.

Thorsten Feldmann, U Siegen

Light-cone distribution amplitude of the B-meson

##### Light-cone distribution amplitudes (LCDAs) for B-mesons in heavy-quark effective theory (HQET) provide one of the essential non-perturbative inputs entering QCD factorization theorems for exclusive B-decays. In this talk, I show how to derive the eigenfunctions of the Lange-Neubert evolution equation which governs the behaviour of the B-meson LCDAs under a change of renormalization scale. The spectrum of the LCDA with respect to these eigenfunctions defines a “dual” function which renormalizes multiplicatively. In terms of these dual functions, renormalization-group improved factorization formulas take a very simple form. I also report on how to implement perturbative constraints from the operator product expansion in HQET within the new formalism.

Stefan Recksiegel, Technische Universitat Munchen

Using dimensional analysis as a measure of fine tuning