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As a theoretical high energy physicist, my broad research interests are in the explorations of strongly interacting quantum field theories that appear in the context of finite temperature field theories, quantum chromodynamics (QCD), and holographic duality conjecture in string theory.
I use both analytical methods and numerical techniques to study the physics of these systems. Lattice Quantum Field Theory and Holography: Certain classes of quantum field theories at strong coupling and finite temperature are equivalent to quantum black hole geometries in dual weakly coupled gravitational theories. Such theories of quantum gravity and black holes arise in particular limits of parameters of certain classes of string theories. This equivalence between string and gauge theories is known as the holographic duality or the AdS/CFT correspondence [1]. Hawking and others famously used semiclassical methods to show that black holes are thermodynamic entities with internal degrees of freedom. This opened up intriguing questions about the constituents of black holes and also led to the famous information loss paradox, which describes the tension between semiclassical and quantum description of black holes. In the recent years there has been a huge resurgence of interest in this area, with the proposal of black hole firewalls, where the semiclassical description of black holes is proposed to break down before one would naively expect. It seems that no resolution of this fierce debate is possible until we have a calculation method which incorporates quantum gravity. Gauge/gravity duality conjecture states that certain classes of gauge theories, known as the Maximally Supersymmetric Yang-Mills (MSYM) theories, in 3+1 and lower spacetime dimensions, are dual to quantum string/gravity theories. The semiclassical quantum gravity limit involves taking a particular large-N limit of MSYM theories, with N counting the color degrees of freedom. In order to describe the features of quantum black holes and the key question on the existence of black firewalls, we need to study the dual gauge theories at finite temperature. Such thermal theories are strongly coupled in practice, and thus analytically intractable. To study them reliably, one needs a first-principles definition based on the regularization of the field theory path integral on a spacetime lattice. Since the MSYM theories have an enlarged symmetry, naive discretization methods fail due to the lack of a discrete subgroup of supersymmetry. Naively discretized theories are no longer supersymmetric and for MSYM theories, it is prohibitively difficult to recover the supersymmetric target theories in the continuum limit. Fortunately, there exists an elegant method called exact lattice supersymmetry. One could discretize MSYM theories on a spacetime lattice, in a consistent way, by exactly preserving a subset of the supersymmetry charges using the methods of twisting and orbifolding [2]. There has been tremendous development in the area of exact lattice supersymmetry in recent years, and this has been the focus of my past and current research. I have contributed significantly to this field and written standard reviews on this topic [3, 4]. I have also taken part in co-developing a state of the art computer program to simulate supersymmetric Yang-Mills theories using Markov Chain Monte Carlo algorithm [5]. I am currently utilizing my expertise and experience in lattice simulations to write more efficient computer programs to simulate large N 3+1 and lower dimensional cases of MSYM theories, with collaborators Simon Catterall (Syracuse University, USA), David Schaich (University of Liverpool, UK), Raghav Jha (Perimeter Institute, Canada), and Toby Wiseman (Imperial College London). We plan to give particular attention to the 0+1 supersymmetric quantum mechanics case (the so-called BFSS and BMN matrix models that appear in the context of string theory), since it is certainly the simplest setting numerically, and it captures all the important questions we have for quantum gravity, and has the most detailed gravity predictions. Significant progress has been made recently on verifying the gauge/gravity duality using numerical simulations of the quantum mechanical system, through approaches based on naive and manifestly supersymmetric lattice regularizations [6]. We plan to verify these results and go further using the improved simulation code developed using the ideas inspired from exact lattice supersymmetry. In the cases of more than 0+1 dimensions, in fact there is not just one type of black hole, but there may be several varieties, in the dual gravitational theories. In the semiclassical gravity, we understand there may be Gregory-Laflamme type of phase transitions between them, which manifests itself as thermal phase transitions at large N in dual gauge theories. I have performed the first lattice simulations of large N 1+1 MSYM on a thermal circle, with Simon Catterall and Toby Wiseman, and we have seen the evidence for a phase transition related to the Gregory-Laflamme transition. Much more work is needed to accurately confirm this, and also to study the higher dimensional examples, and explorations in these directions are part of the near-future goals. It would be interesting to have lattice formulations of supersymmetric Yang-Mills theories with more exotic field contents. Theories with matter fields in fundamental and anti-fundamental representations would capture the physics of theories that are closer to Quantum Chromodynamics (QCD). It is also interesting to formulate lattice field theories with more exotic matter representations (such as two-index) that would serve as candidate theories for dark matter particles. Another type of lattice formulation that I am interested in is that of supersymmetric quiver gauge theories. Such theories have realizations as intersecting brane geometries in string theory. They also play a major role in understanding dualities in three-dimensional field theories. Two-dimensional quiver gauge theories can be related to quantum integrable systems, such as spin chains, through the gauge/Bethe correspondence. It would also be interesting to perform non-perturbative investigations of four-dimensional supersymmetric Yang-Mills theories with lesser amount of supersymmetry such as the N = 2* and N = 1* gauge theories. Recently, we have constructed a lattice version of four-dimensional N = 2* super Yang-Mills theory that preserves one supersymmetry charge at finite lattice spacing [7]. Such theories exhibit a rich phase structure and are more related to phenomenologically interesting supersymmetric QCD type of theories. Quantum Field Theories with Complex Actions: A standard tool to investigate numerous nonperturbative features of quantum field theoretic systems is the Monte Carlo simulations of a lattice regularized version of the field theory path integral. The fundamental idea behind path integral Monte Carlo is to generate field configurations with a probability weight given by the exponential of the negative of the action (in Euclidean spacetime) and then compute the path integral by statistically averaging these importance sampled ensemble of field configurations. However, when the action is complex, for example, when studying QCD at finite temperature and baryon/quark chemical potential, QCD with a theta term, Chern-Simons gauge theories, or chiral gauge theories, the fermion determinant of the theory can be complex, and this feature results in the so-called sign problem (or a phase problem to be more exact). In the context of string theory, the IKKT matrix model, a zero-dimensional supersymmetric quantum field theory that serves as a promising candidate for a nonperturbative formulation of superstring theory, is shown to have a complex fermion operator [8, 9]. This results in simulation algorithms based on path integral Monte Carlo unreliable. There exist several methods that can can handle the sign problem. These include methods such as analytical continuation, Taylor series expansion [10], methods based on the complexification of the integration variables such as the Lefschetz thimble method [11] and complex Langevin method (CLM) [12, 13]. The CLM is a straightforward generalization of the real Langevin method and it extends the idea of stochastic quantization for ordinary field theoretic systems with real actions to the cases with complex actions. It overcomes the sign problem by defining a stochastic process, with complexified field variables, using Langevin equations for the complex action. The expectation values of observables in the original path integral are then calculated from an average of the corresponding quantities over this stochastic process. CLM has been used successfully in various models in the recent past. There have also been studies of supersymmetric models based on CLM. In Ref. [14, 8], using complex Langevin simulations, the Gross-Witten-Wadia (GWW) [15, 16] phase transitions in certain large-N matrix models were observed. Recently, in Ref. [17] we looked at certain classes of zero-dimensional quantum field theories with complex actions using CLM method to probe nonperturbative SUSY breaking in these models. In our recent work [18], we made use of CLM to study dynamical SUSY breaking in supersymmetric quantum mechanics models with complex actions. They also include the interesting case of theories exhibiting PT symmetry. The central theme of stochastic quantization is that expectation values of observables are obtained as equilibrium values of a stochastic process. In Langevin dynamics, this is implemented by evolving the system in a fictitious time direction, the Langevin time, subject to a stochastic noise. We could think of applying Langevin dynamics when the actions under consideration are complex. In such cases, the field variables become complexified during the Langevin evolution since the gradient of the action, the drift term, is complex. When the action is real, it can be shown that in the limit of large Langevin time, the stationary solution of the Fokker-Planck equation will be reached guaranteeing convergence of the Langevin dynamics to the correct equilibrium distribution. When the action is complex we will end up in a not so easy situation. The drift term will be complex and thus, if we consider Langevin dynamics based on the above equation, we will end up with complexified fields. We can still consider Langevin dynamics with complex probabilities but proofs towards convergence to the complex weight (the exponential of the negative of the action) will be non-trivial. Another recent and developing method to deal with quantum field theories with complex actions uses the complex analog of Morse theory from differential topology [19]. There, the objects of primary interest, the so-called Lefschetz thimbles, are a set of sub-manifolds associated with a function that satisfy the Morse flow equation for the real part of the function. The central idea behind using this formalism is to recast the path integral in terms of a finite set of non-oscillatory integrals. Recently we explored zero-dimensional scalar field theories with complex actions, containing a quartic interaction term and a source term [20]. These models represent the simplest nontrivial quantum field theory with a linear source term. We showed that the Lefschetz thimble equations can be derived, using first principles, for various values of the coupling parameters. Another result we obtained in this work is the analytic expressions for the combined intersection number of thimbles and anti-thimbles of these zero-dimensional theories. We also provided a completely analytic demonstration of the existence of quantum phases (or quantum critical points) in the model using the intersection numbers. Due to the lack of existence of a proper definition of thermodynamic quantities in zero dimensions, the discussion is formulated in terms of non-analytic behavior of the partition function. In the near future, we hope to extend these calculations to the more realistic cases such as finite temperature QCD with chemical potential and thus give input to heavy-iron collision experiments at LHC and RHIC. References
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Anosh Joseph 