Scientific Series

We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with fixed (induced) boundary metric. By solving the constraints in a constant-mean-curvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientation-preserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that have the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required --- in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham's group-theoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group, and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.

Zoom link:  https://pitp.zoom.us/j/94369372201?pwd=NWNsYno3RmZIWUx0LytWZ09PVDVVQT09

Every unitary map with a factorisation of domain and codomain into subsystems has a well-defined causal structure given by the set of influence relations between its input and output subsystems. A causal decomposition of a unitary map U is, roughly, one that makes all there is to know about U in terms of causal structure evident and understandable in compositional terms. We'll argue that this is more than just about drawing more intuitive pictures for the causal structure of U -- it is about really understanding it at all. Now, it has been known for a while that decompositions in terms of ordinary circuit diagrams do not suffice to this end and that at least so called 'extended circuit diagrams', or 'routed circuit diagrams' are necessary, revealing a close connection between causal structure and algebraic structures that involve a particular interplay of direct sum and tensor product. Though whether or not these sorts of routed circuit diagrams suffice has been an open question since. I will give an introduction and overview of this business of causal decompositions of unitary maps, and share what is an on-going thriller.

Zoom link:  https://pitp.zoom.us/j/95689128162?pwd=RFNqWlVHMFV0RjRaakszSTBsWkZkUT09

The aim of the presentation is to review the beautiful geometry underlying the standard model of particle physics, as captured by the framework of "SO(10) grand unification." Some new observations related to how the Standard Model (SM) gauge group sits inside SO(10) will also be described. 

I will start by reviewing the SM fermion content, organising the description in terms of 2-component spinors, which give the cleanest picture. 

I will then explain a simple and concrete way to understand how spinors work in 2n dimensions, based on the algebra of differential forms in n dimensions.

This will be followed by an explanation of how a single generation of standard model fermions (including the right-handed neutrino) is perfectly described by a spinor in a 10 ("internal") dimensions. 

I will review how the two other most famous "unification" groups -- the SU(5) of Georgi-Glashow and the SO(6)xSO(4) of Pati-Salam -- sit inside SO(10), and how the SM symmetry group arises as the intersection of these two groups, when they are suitably aligned.

I will end by explaining the more recent observation that the choice of this alignment, and thus the choice of the SM symmetry group inside SO(10), is basically the choice of two Georgi-Glashow SU(5) such that the associated complex structures in R^{10} commute. This means that the SM gauge group arises from SO(10) once a "bihermitian" geometry in R^{10} is chosen. I will end with speculations as to what this geometric picture may be pointing to. 

Zoom link:  https://pitp.zoom.us/j/95984379422?pwd=SE1ybktzQzcreWREblhEUkZWWElMUT09

We study the behavior of errors in the quantum simulation of  spin systems with long-range multibody interactions resulting from the  Trotter-Suzuki decomposition of the time evolution operator. We  identify a regime where the Floquet operator underlying the Trotter  decomposition undergoes sharp changes even for small variations in the  simulation step size. This results in a time evolution operator that  is very different from the dynamics generated by the targeted  Hamiltonian, which leads to a proliferation of errors in the quantum  simulation. These regions of sharp change in the Floquet operator,  referred to as structural instability regions, appear typically at  intermediate Trotter step sizes and in the weakly interacting regime,  and are thus complementary to recently revealed quantum chaotic  regimes of the Trotterized evolution [L. M. Sieberer et al. npj  Quantum Inf. 5, 78 (2019); M. Heyl, P. Hauke, and P. Zoller, Sci. Adv.  5, eaau8342 (2019)]. We characterize these structural instability  regimes in p-spin models, transverse-field Ising models with  all-to-all p-body interactions, and analytically predict their  occurrence based on unitary perturbation theory. We further show that  the effective Hamiltonian associated with the Trotter decomposition of  the unitary time-evolution operator, when the Trotter step size is  chosen to be in the structural instability region, is very different  from the target Hamiltonian, which explains the large errors that can  occur in the simulation in the regions of instability. These results  have implications for the reliability of near-term gate based quantum  simulators, and reveal an important interplay between errors and the  physical properties of the system being simulated.

Zoom link:  https://pitp.zoom.us/j/92045582127?pwd=WDUxcnlIeXdnVWM3WGJoSFVMNDE2dz09

The Berry phase, discovered by M.V. Berry in 1984, has been applied to the construction of various invariants in topological phase of matters. The Berry phase measures the non-triviality of a uniquely gapped system as a family and takes its value in $H^2({parameter space};Z)$.

In recent years, there have been several attempts to generalize it to higher-dimensional many-body lattice systems[1,2,3,4], called the “higher” Berry phase. In the case of spatial dimension d it is believed that the higher Berry phase takes its value in $H^{d+2}({parameter space};Z)$. However, in general dimensions, the definition of the higher Berry phase in lattice systems is not yet known.

In my talk, I’ll explain about the way to extract the higher Berry phase in 1-dimensional systems by using the “higher inner product” of three matrix product states and how to construct the topological invariant which takes its value in $H^3({parameter space};Z)$. This talk is based on [3] and [4].

Refs:
[1] A. Kapustin and L. Spodyneiko Phys. Rev. B 101, 235130
[2] X. Wen, M. Qi, A. Beaudry, J. Moreno, M. J. Pflaum, D. Spiegel, A. Vishwanath and M. Hermele arXiv:2112.07748
[3] S. Ohyama, Y. Terashima and  K. Shiozaki arXiv:2303.04252
[4] S. Ohyama and S. Ryu arXiv:2304.05356  

Zoom link:  https://pitp.zoom.us/j/93720709850?pwd=RTliMDNMRWo2V2k1MnBKUjlRMjBqZz09

Taking string theory off shell requires breaking Weyl invariance on the worldsheet, i.e. the worldsheet theory is now a QFT instead of a CFT. I will explain Tseytlin’s first-quantized approach to taking the worldsheet theory off-shell in a consistent manner, with a particular emphasis on the subtleties involved in calculating the sphere amplitude. This approach allows for the derivation of a classical string action which gives rise to the correct equations of motion and S-matrix, to all orders in perturbation theory. 

I'll also explain the underlying conceptual structure of the Susskind and Uglum black hole entropy argument. There I will show explicitly how the classical (tree-level) effective action and entropy S = A/4G_N may be calculated from the sphere diagrams. 

Time permitting, I will discuss ongoing efforts to derive the Ryu-Takayanagi formula in string theory.

Based on arXiv:2211.08607 and arXiv:2211.16448. 

Zoom link:  https://pitp.zoom.us/j/93668017324?pwd=K2pxZEhjalRTWkVVbVRESCtRVDFmUT09

The mixing angles of the quark sectors are constrained by unitarity in the standard model. However, recent data indicates a about 3 sigma deviation from unitarity in the mixing angle between the 1st and 2nd generation down-type quarks, known as the Cabibbo angle anomaly. The observations include the charged-current weak decays of neutrons, nuclei, kaons, and the hadronic decay of tau leptons. Although the issue appears to lie in the quark sector, modifying the neutrino sector may offer a solution. In this talk, we discuss recent findings that suggest a sterile neutrino of MeV mass mixing with the electron-type neutrino can resolve the Cabibbo angle anomaly. We also examine the current bounds and future prospects of this scenario.

Zoom Link:  https://pitp.zoom.us/j/98083942792?pwd=eHFRUmJUVGNJcVpTSHZXVXFKQm95QT09

The astrophysical stochastic gravitational wave background (SGWB) originates from numerous faint sub-threshold  gravitational wave (GW) signals arising from the coalescing binary compact objects. This background is expected to be discovered from the current (or next-generation) network of GW detectors by cross-correlating the signal between multiple pairs of GW detectors. However, detecting this signal is challenging and the correlation is only detectable at low frequencies due to the arrival time delay between different detectors. In this work, we propose a novel technique, Spectrogram Correlated Stacking (or SpeCS), which goes beyond the usual cross-correlation (and to higher frequencies)  by exploiting the higher-order statistics in the time-frequency domain which accounts for the chirping nature of the individual events that comprise SGWB.

We show that SpeCS improves the signal-to-noise for the detection of SGWB by up to an order of magnitude, compared to standard optimal cross-correlation methods which are tuned to measure only the power spectrum of the SGWB signal. SpeCS can probe beyond the power spectrum and its application to the GW data available from the current and next-generation GW detectors would speed up the SGWB discovery. 

based on work with Ramit Dey, Luis Longo, and Suvodip Mukherjee

Zoom link:   https://pitp.zoom.us/j/97091817158?pwd=MHNkdjFQT0plVzJJY2lsOHRxdDdwdz09

I will first review the construction of quiver Yangians for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds; they serve as BPS algebras of these systems and their characters reproduce the unrefined BPS indices. I will then explain how to generalize the construction to arbitrary quivers and how to incorporate refined BPS indices. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies. Time permitting, I will discuss some applications, such as on BPS counting and on Gauge/Bethe correspondence. 

Zoom link:  https://pitp.zoom.us/j/96812116687?pwd=RjlsSVhDaUVBREtUUnd5S04rQjhpZz09

I will discuss several issues related to the computation of Poisson brackets in field theories. I will show that by choosing appropriate functional spaces as configuration manifolds, it is possible to avoid the use of distributions. This is relevant, for instance, in the context of Loop Quantum Gravity, where the basic holonomy/flux variables play a central role. I will illustrate the main ideas by using simple examples based on Sobolev spaces.

Zoom link:  https://pitp.zoom.us/j/92794475242?pwd=T2Fjbk1lTXRCNnBxVDZabnJqWlAzUT09

Highly magnetized neutron stars are a source of extreme transients observed in different bands, like the fast radio burst (FRB) and associated hard X-ray burst from the Galactic magnetar SGR 1935+2154. The origin of such outbursts, hard X-rays on the one hand and millisecond duration FRBs on the other hand, is still unknown. We present a global model for various kinds of such magnetar outbursting activities. Crustal surface motions are expected to twist the inner magnetar magnetosphere by shifting the frozen-in footpoints of magnetic field lines. We discuss criteria for the development of various instabilities of 3D twisted flux bundles in the force-free dipolar magnetospheres and compare their energetic properties to observations of magnetar X-ray flares. We then review a recently developed FRB generation mechanism in the outer magnetosphere of a magnetar. The strong magnetic pulse induced by a magnetar flare collides with the current sheet of the magnetar wind, compresses and fragments it into a self-similar chain of magnetic islands. Time-dependent plasma currents created during their collisions produce relatively narrow-band GHz emission with luminosities sufficient to explain bright extragalactic FRBs.

Zoom ink:  https://pitp.zoom.us/j/96469987183?pwd=N1UzVkh6RGZUeWV6TFZJLzk0M3VWZz09