Generalised symmetries, anomalous magnetohydrodynamics and holography

In this thesis we study the finite temperature physics of a system which is afflicted by the Adler-Bell-Jackiw anomaly or, the chiral anomaly. The universality class of such systems are commonly referred to as the {\it chiral plasma}. Its weakly coupled physics is described by a theory of massless Dirac fermions coupled to dynamical electromagnetism and hence the universal symmetry structure of the {\it chiral plasma} is that of dynamical $U(1)$ Abelian gauge theory with charged matter. In this theory, the non-conservation of the axial current due to the chiral anomaly is given by a dynamical operator $f_{\mu\nu} \tilde{f}^{\mu\nu}$ constructed from the field-strength tensor. We attempt to describe this physics in a universal manner by casting this operator in terms of the 2-form current for the 1-form symmetry associated with magnetic flux conservation. The precise symmetry structure in encoded by the anomaly equation which can be formulated as the intertwining of these two currents. The sense in which this is universal is that it is preserved along RG flows. Utilising this universal structure we first perform a holographic investigation of this system and then construct a hydrodynamic effective action for it. This effective action can be understood as ``an action" for {\it chiral magnetohydrodynamics}, which is devoted to understanding the long-distance, late-time behavior of such a system suffering from an ABJ anomaly. To perform the holographic study, we first construct a dual bulk theory with the aformentioned symmetry breaking pattern and study some aspects of finite temperature anomalous magnetohydrodynamics. We explicitly calculate the charge susceptibility and the axial charge relaxation rate as a function of temperature and magnetic field and compare to recent lattice results. At small magnetic fields we find agreement with elementary hydrodynamics weakly coupled to an electrodynamic sector, but we find deviations at larger fields. Next we consider chiral magnetohydrodynamics. Using the universal symmetry structure encoded in the anomaly we write down ``effective actions" capturing the equilibrium physics and the physics of dissipation. We present Euclidean generating functional and dissipative action approaches to the dynamics and reproduce some aspects of known chiral MHD phenomenology from an effective theory viewpoint, including the chiral separation and magnetic effects. We also discuss the construction of the {\it non-invertible} axial symmetry defect operators in our formalism in real time. Finally, to study the axial charge relaxation rate in the limit of vanishing magnetic field, we undertake a study to see if hydrodynamic fluctuations affect this rate. We compute the finite-frequency real-time topological susceptibility arising from magnetohydrodynamic fluctuations. We find that it vanishes at zero frequency, indicating that the axial charge dissipation rate vanishes at zero background magnetic field. This is probably suggestive of the fact that the symmetry structure encoded in the anomaly is protected by the non-invertible defect operators as 1-loop effects do not spoil it

Two- & Three-character solutions to MLDEs and Ramanujan-Eisenstein Identities for Fricke Groups

In this work we extend the study of arXiv:2210.07186 by investigating two- and three-character MLDEs for Fricke groups at prime levels. We have constructed these higher-character MLDEs by using a $\mathit{novel}$ Serre-Ramanujan type derivative operator which maps $k$-forms to $(k+2)$-forms in $\Gamma^{+}_0(p)$. We found that this $\mathit{novel}$ derivative construction enabled us to write down a general prescription for obtaining $\mathit{Ramanujan-Eisenstein}$ identities for these groups. We discovered several $\mathit{novel}$ single-, two-, and three-character admissible solutions for Fricke groups at levels $2$ and $3$ after solving the MLDEs among which we have realized some in terms of Mckay-Thompson series and others in terms of modular forms of the corresponding Hecke groups. Among these solutions, we have identified interesting non-trivial bilinear identities. Furthermore, we could construct $\mathit{putative}$ partition functions for these theories based on these bilinear pairings, which could have a range of lattice interpretations. We also present and discuss modular re-parameterization of MLDE and their solutions for Fricke groups of prime levels.Comment: 94 pages + 14 pages (appendices and references); 3 figures; 13 table

New meromorphic CFTs from cosets

In recent years it has been understood that new rational CFTs can be discovered by applying the coset construction to meromorphic CFTs. Here we turn this approach around and show that the coset construction, together with the classification of meromorphic CFT with c ≤ 24, can be used to predict the existence of new meromorphic CFTs with c ≥ 32 whose Kac-Moody algebras are non-simply-laced and/or at levels greater than 1. This implies they are non-lattice theories. Using three-character coset relations, we propose 34 infinite series of meromorphic theories with arbitrarily large central charge, as well as 46 theories at c = 32 and c = 40

Higher-form symmetry and chiral transport in real-time lattice U(1)U(1) gauge theory

We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma -- defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD -- remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.Comment: 24 pages with appendix, 9 figures. Comments are welcome

ASSESSMENT OF SUSTAINABILITY INDICATORS OF TWO GAS- TURBINE PLANTS WITH NAPHTHA AND NAPHTHA-RFG MIXTURE AS FUELS

To enhance sustainability of any energy system exergy based sustainability indicators (exergy efficiency, waste exergy ratio, environmental effect factor and exergetic sustainability index) are used. In the present paper sustainability aspects of two GT based power plant are carried out using sustainability indicators. For this purpose, two GT1) configurations, case A (Naphtha based GT power plant) and case B (Naphtha-Residual fuel gas mixture GT 2) are taken up as case study. Results show that exergetic sustainability index obtained as for case A is higher as compared to case B

Modular Differential Equations with Movable Poles and Admissible RCFT Characters

Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach.Comment: 81 pages, 4 figures, 2 table

Modular differential equations with movable poles and admissible RCFT characters

Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach

Where to Focus on for Human Action Recognition?

International audienceIn this paper, we present a new attention model for the recognition of human action from RGB-D videos. We propose an attention mechanism based on 3D articulated pose. The objective is to focus on the most relevant body parts involved in the action. For action classification, we propose a classification network compounded of spatio-temporal sub-networks modeling the appearance of human body parts and RNN attention subnetwork implementing our attention mechanism. Furthermore, we train our proposed network end-to-end using a regularized cross-entropy loss, leading to a joint training of the RNN delivering attention globally to the whole set of spatio-temporal features, extracted from 3D ConvNets. Our method outperforms the State-of-the-art methods on the largest human activity recognition dataset available to-date (NTU RGB+D Dataset) which is also multi-views and on a human action recognition dataset with object interaction (Northwestern-UCLA Multiview Action 3D Dataset)