Conformal field theories are characterized by structure constants (3-point correlation functions). In order for the theory to be consistent, the structure constants must satisfy the “bootstrap equation”, which is useful to numerically solve, for example, for the critical exponent of the 3d Ising model. From a mathematical point of view, the bootstrap equation arises from the operad structure of spacetime, and such mathematics may be useful to find (as yet undiscovered) constraints on quantum field theory. In this talk, we will introduce the notion of operad and discuss the relation between operads and operator product expansions based on mathematical studies of conformal field theories in two dimensions.

The IKKT matrix model is viewed as a gauge theory of space-time and matter, which arises through an analog of the Higgs effect on suitable vacua, describing 3+1 dimensional space-time branes in the weak coupling regime. In particular, we consider vacua where the SO(9,1) invariance is spontaneously broken to SO(3,1). These vacua describe a cosmological FLRW space-time, on which (an extended version of) gravity arises through quantum effects. Some progress towards understanding the resulting physics is discussed.

On February 23, 1987, neutrinos from a supernova explosion in the Large Magellanic Cloud were observed for the first time in the world. Observations of supernova neutrinos, which are emitted from supernova explosions caused by gravitational collapse at the center of massive stars during the final stage of their evolution, are important for various topics in astrophysics, including the history of star formation and the mechanism of supernova explosions. Therefore, supernova neutrinos have been actively studied both observationally and theoretically. In particular, Super-Kamiokande, which which began a new stage of operations as SK-Gd in 2020, is expected to bring drastic progress in supernova neutrino research, especially in the measurement of diffuse supernova neutrino background and the pointing accuracy for nearby supernovae. Furthermore, next-generation large neutrino detectors such as Hyper-Kamiokande will enter a new stage of precision measurements for supernova neutrino observations.
In this seminar, I will discuss recent progress and prospects of supernova neutrino research.

The strong CP problem can be solved by parity symmetry with extended gauge symmetry. We first review two classes of models: the ones with the minimal fermion content and the ones with the minimal Higgs content. We then focus on the latter class of models and discuss a dark matter model where the stability of dark matter accidentally arrises from the extended gauge symmetry. The enough stability of dark matter provides an upper bound on the parity symmetry breaking scale. We then discuss a neutrino mass model and show that in the minimal model the neutrino mass is generated by quantum corrections. New gauge-singlet fermions in the model may be discovered by near-future experiments.

Neutrinoless double beta decay is the primary means with which we can probe a potential Majorana nature of light neutrinos. Planned experiments searching for this hypothetical decay aim to be sensitive to half-lives of up to 10^28 years, allowing to probe Majorana neutrino mass scales of O(10 meV). It is also well established that neutrinoless double beta decay receives contributions beyond light neutrino exchange in New Physics scenarios beyond the Standard Model (SM) that incorporate lepton number violation, such as sterile Majorana neutrinos and R-Parity violating supersymmetry. After briefly reviewing neutrinoless double beta decay and its interpretations, I will motivate the use of two-neutrino double beta decay to probe for exotic physics as well. This decay, allowed in the SM and observed in several isotopes, is typically considered background to neutrinoless double beta decay searches. Besides allowing insights into nuclear matrix elements it can also be used to search for New Physics, though, due to high event statistics in current and future double beta decay searches. In this context, I will discuss modifications of the double beta decay spectrum due to exotic particle emission (such as kinks from sterile neutrinos), exotic currents beyond V-A and neutrino self-interactions, motivating the search for such scenarios.

I will discuss the role of inclusive and exclusive b-> c(u) l nu decays in the extractions of $|V_{cb}|$ and $|V_{ub}|$. I will update the precision extractions of the observables associated with a few related exclusive decay modes. Also, I will focus on the possible role of the available data on these decays in constraining the parameters associated with the new interactions beyond the SM.

Universal dynamics associated with scale-invariant properties has garnered much attention in the field of statistical mechanics for a long time. Thanks to the high controllability of ultracold atom experiments, such universal quantum dynamics has been studied theoretically and experimentally over a decade from the perspective of nonthermal fixed points, which was originally introduced in the context of high-energy physics. In this talk, we will begin with an introduction to ultracold atoms, reviewing applications of nonthermal fixed points to ultracold atoms by showing recent theoretical and experimental achievements.

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There is no empirical evidence for CP conservation in the strong interactions. As there generally is a renormalizable, parity-odd coupling between the field strength and its dual, this requires an explanation from theory.
I will therefore first review what interactions are present when constructing an effective theory for hadrons from QCD. But I will also point out, that from such considerations alone, it cannot be decided whether the effective interactions (that, e.g., give mass to eta-prime) are misaligned (CP violation) or aligned (no CP violation) with the quark mass phase.
To see whether or not there is a material effect of the parity-odd operator in QCD requires therefore an understanding of how field configurations from different topological sectors contribute to the path integral or, in canonical quantization, whether topology implies different ground states that are in general not parity eigenstates. To that end, I will review the pertinent homeomorphisms between the SU(2) subgroups of the strong interactions and the boundaries of spacetime or spatial hypersurfaces.
As for the Euclidean path integral approach, I will note that pure gauge configurations on the boundary only follow when the latter is placed at infinity. Picard-Lefschetz theory then implies that steepest-descent integration contours cover all field configurations within a topological sector that one can find in the infinite spacetime volume. Consequently, the limit of infinite spacetime volume must be taken before summing over sectors, and it turns out that parity violation then vanishes. Commuting these limits, as tacitly done in standard approaches, corresponds to a singular deformation of the original Cauchy contour, falsely suggesting parity-violating results.
Regarding canonical quantization, I will note that the usually considered theta-vacua are not properly normalizable, which is at odds with the probability interpretation from the axioms of quantum mechanics. The root of this problem is the summation over gauge-redundant configurations in the orthonormality relations among theta-vacua. Imposing that (in temporal gauge) the wave functionals and Hilbert-space operators are well-defined when the inner product covers each physical field configuration one time and one time only, I recover that the consistent states satisfy Gauß’ law and are moreover eigenstates of parity.
References:
2001.07152 [hep-th]
2403.00747 [hep-th]
2404.16026 [hep-ph]

In this talk, we will explore the fundamental Kazakov-Migdal (FKM) model on a generic graph, where the partition function is represented by the Ihara zeta function weighted by unitary matrices. The effective action of the FKM model is described by a summation of all Wilson loops on the graph, which can be regarded as an extension of the usual Wilson action in lattice gauge theory. We show that the FKM model on regular graphs exhibits an exact strong/weak coupling duality, reflecting the functional equation of the Ihara zeta function. Although this duality is not precise for irregular graphs, we show that the effective action in the large coupling region can also be represented by a summation of Wilson loops, similar to that in the small coupling region. We also discuss the stability of the model and show that the FKM model becomes unstable in the critical strip of the Ihara zeta function. Interestingly, the FKM model universally exhibits the so-called Gross-Witten-Wadia (GWW) phase transitions. By comparing the FKM model with the GWW model, we estimate the phase structure of the FKM model in both small and large coupling regions, which is validated through numerical simulations. For the benefit of graduate students, we will begin the seminar with an introductory explanation of lattice gauge theory and graph theory, providing a foundation for understanding the subsequent discussion.