Discrete symmetries are important in physics beyond the Standard Model. One example is the introduction of R-parity in the MSSM to suppress operators leading to exceedingly fast proton decay. In this talk we would like to introduce the study of discrete gauge symmetries in brane models.

## The lowest excited configuration of harmonium

The harmonium model has long been regarded as an exactly solvable laboratory bench for quantum chemistry [1]. For studying correlation energy, only the ground state of the system has received consideration heretofore. This is a spin singlet state. In this work we exhaustively study the lowest excited (spin triplet) harmonium state, with the main purpose of revisiting the relation between entanglement measures and correlation energy for these quite different species. The task is made easier by working with Wigner quasiprobabilities on phase space.

[1] W. Heisenberg Z. Phys. 38 411 (1926).

## Dilatation Symmetric Scalar-Tensor Theories of Quantum Gravity

The functional renormalization group is utilized to formulate a quantum theory of dilaton gravity that is renormalizable on a non-perturbative level. In the limit where the scalar field’s magnitude is much larger than the renormalization scale, a set of closed β-functions is revealed which accounts for a trivial fixed point scenario. Therein, only the order independent of the scalar field remains nonzero, corresponding to an Einstein-Hilbert truncation with an additional kinetic term for the scalar field.

Specializing to dilatation symmetric effective actions, we propose a new fixed point scenario that respects the symmetry and is exact for the scale k approaching 0. It comprises only the coupling of the scalar field to gravity admissible by the symmetry with no scalar potential, thus having much simpler infrared structure than the usual Einstein-Hilbert action. Moreover, fixed point candidates for the opposing limit are examined. The renormalization group flows are shown to diverge for conformal coupling parameters, thereby realizing the Weyl anomaly. Physical implications are discussed and suggestions for subsequent research are given.

## Holographic Flow of Anomalous transport coefficients

We study the holographic flow of anomalous conductivities induced by gauge and gravitational Chern-Simons terms. We find that the contribution from the gauge Chern-Simons term gives rise to a flow that can be interpreted in terms of an effective, cutoff dependent chemical potential. In contrast the contribution of the gauge-gravitational Chern-Simons term is just the temperature squared and does not flow.

## Massive Gravity

Einstein’s theory of general relativity (GR) is an elegant and experimentally well tested theory of gravity. From this point of view it may not be too surprising that modifying GR will lead to trouble. This talk will review some of the difficulties in different theoretical approaches of giving the graviton a small mass and some the recent successes in this direction. In particular, the focus will be on three dimensional higher-derivative models of massive gravity. When considered at a critical point in their parameter space, these models become the duals of logarithmic conformal field theories.

## Higher derivative Wess Zumino model in three dimensions

We deform the well-known three dimensional N=1 Wess-Zumino model by adding to it higher derivative operators (Lee-Wick operators). The effect of these operators is investigated both at classical and quantum levels.

## Identifying the GM Raman Peak for a single tube by Resonance Raman

The Raman resonance happens when the electronic transition energy Eii meets either the incident laser energy or the scattering photon energy, which leads to the fact that for a single tube, then incident laser energy for RBM resonance doesn’t lie at Eii, but somewhere between Eii and Eii+-Eph, with Eph the phonon mode energy. Due to the large GM phonon energy compared to the RBM one, the RBM and GM for a single tube tend not to share the same resonance condition and a GM profile at a certain incident energy tends to contain unneglectable contributions of tubes with several chiralities even when one of them is in resonance.

## Nonlinear Field Theory with Topological Solitons: Skyrme Models

In this talk, we will give a new insight into one of the most well-known nonlinear field theories, the Skyrme model. We will present some exact relevant solutions coming from different new versions (as gauged BPS baby as well as vector BPS Skyrme models [1]) giving rise to topological solitons, and highlighting the BPS character of the theory.

[1] C. Adam et al, Phys. Rev. D 86 045010, 045015 and to be published (2012).

## NONLINEAR FIELD THEORY WITH TOPOLOGICAL SOLITONS: SKYRME MODELS

In this talk, we will give a new insight into one of the most well-known nonlinear ﬁeld theories, the Skyrme model. We will present some exact relevant solutions coming from diﬀerent new versions (as gauged BPS baby as well as vector BPS Skyrme models [1]) giving rise to topological solitons, and highlighting the BPS character of the theory.

[1] C. Adam et al, Phys. Rev. D 86 045010, 045015 and to be published (2012).

## The phonon theory of liquid matter

Research into liquids has a long history starting from the same time when the theory of gases was developed, forming the basis for our current understanding of the gas state of matter. Yet no theory of liquid heat capacity currently exists, contrary to gases or, for that matter, solids. The perceived difficulty is that interactions in a liquid are both strong and system-specific, implying that the energy strongly depends on the liquid type and that, therefore, liquid energy can not be calculated in general form. We develop a phonon theory of liquids where this problem is avoided. The theory covers both classical and quantum regimes. We demonstrate good agreement of calculated and experimental heat capacity of 21 liquids, including noble, metallic, molecular and hydrogen-bonded network liquids in a wide range of temperature and pressure.