High Energy Physics Theory

An exact formula that relates standard zeta functions and so-called hatted zeta functions in all orders of perturbation theory is presented. This formula is based on the Landau-Khalatnikov-Fradkin transformation

Certain CFTs with a globalU(1)symmetry become superfluids when coupled to a chemical potential. When this happens, a Goldstone effective field theory controls the spectrum and correlators of the lightest large charge operators. We show that in 3d, this EFT contains a single parity-violating 1-derivative term with quantized coefficient. This term forces the superfluid ground state to have vortices on the sphere, leading to a spectrum of large charge operators that is remarkably richer than in parity-invariant CFTs. We test our predictions in a weakly coupled Chern-Simons matter theory.

In this note we study CFT2Virasoro conformal blocks with heavy operators in the large-climit in the context of AdS3/CFT2correspondence. We compute the lengths of the holographic Steiner trees dual to the5-point and6-point conformal blocks using the superlight approximation when one or more dimensions are much less than the others. These results are generalized forN-point holographic Steiner trees dual to(N+1)-point conformal blocks with superlight weights.

In this work, we try to construct the Lax connections ofTT¯-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in theTT¯-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.

The canonical forms associated to scattering amplitudes of planar Feynman diagrams are interpreted in terms of masses of projectives, defined as the modulus of their central charges, in the hearts of certaint-structures of derived categories of quiver representations and, equivalently, in terms of cluster tilting objects of the corresponding cluster categories.

The Swampland program aims to determine the constraints that an effective field theory must satisfy to be consistent with a UV embedding in a quantum gravity theory. Different proposals have been formulated in the form of Swampland conjectures. In these lecture notes, we provide a pedagogical introduction to the most important Swampland conjectures, their connections and their realization in string theory compactifications. The notes are based on the series of lectures given by Irene Valenzuela at the online QFT and Geometry summer school in July 2020.

Berry's phase, which is associated with the slow cyclic motion with a finite period, looks like a Dirac monopole when seen from far away but smoothly changes to a dipole near the level crossing point in the parameter space in an exactly solvable model. This topology change of Berry's phase is visualized as a result of lensing effect; the monopole supposed to be located at the level crossing point appears at the displaced point when the variables of the model deviate from the precisely adiabatic movement. The effective magnetic field generated by Berry's phase is determined by a simple geometrical consideration of the magnetic flux coming from the displaced Dirac monopole.

Given a D-brane background in string theory (or equivalently boundary conditions in a two-dimensional conformal field theory), classical solutions of open string field theory equations of motion are conjectured to describe new D-brane backgrounds (boundary conditions). In this thesis, we study these solutions in bosonic open string field theory using the level truncation approach, which is a numerical approach where the string field is truncated to a finite number of degrees of freedom.We start with a review of the theoretical background and numerical methods which are needed in the level truncation approach and then we discuss solutions on several different backgrounds. First, we discuss universal solutions, which do not depend on the open string background, then we analyze solutions of the free boson theory compactified on a circle or on a torus, then marginal solutions in three different approaches and finally solutions in theories which include the A-series of Virasoro minimal models. In addition to known D-branes, we find so-called exotic solutions which potentially describe yet unknown boundary states.This paper is based on my doctoral thesis submitted to the Faculty of Mathematics and Physics at Charles University in Prague.

It is well-known that principal bundles and associated bundles underlie the geometric structure of classical gauge field theories. In this paper, we explore the reformulation of gauge theories in terms of Lie algebroids and their associated bundles. This turns out to be a simple but elegant change, mathematically involving a quotient that removes spurious structure. The payoff is that the entire geometric structure involves only vector bundles over space-time, and we emphasize that familiar concepts such as BRST are built into the geometry, rather than appearing as adjunct structure. Thus the formulation of gauge theories in terms of Lie algebroids provides a fully off-shell account of the BRST complex. We expect that this formulation will have appealing impacts on the geometric understanding of quantization and anomalies, as well as entanglement in gauge theories. The formalism covers all gauge theories, and we discuss Yang-Mills theories with matter as well as gravitational theories explicitly.

We disclose the effects of Lifshitz dynamical exponentzon the properties of holographic paramagnetic-ferromagnetic phase transition in the background of 4D and 5D Lifshitz spacetime. To preserve the conformally invariance in higher dimensions, we consider the Power-Maxwell (PM) electrodynamics as our gauge field. We introduce a massive2-form coupled to the PM field and perform the numerical shooting method in the probe limit by assuming the PM and the2-form fields do not back react on the background geometry. The results indicate that the critical temperature decreases with increasing the strength of the power parameterqand dynamical exponentz. Besides, the formation of magnetic moment in the black hole background is harder in the absence of an external magnetic field. At low temperatures, when there is no external magnetic field, our result show the spontaneous magnetization and the ferromagnetic phase transition. We find that the critical exponent has its universal value ofβ=1/2regardless of the parametersq,zas well as dimension d, which is in agreement with the result of the mean field theory. In the presence of external magnetic field, the magnetic susceptibility satisfies the Cure-Weiss law.