Talk details

Talk 1: Fractons from higher-form symmetries and non-Riemannian geometry

Fracton phases are novel phases of matter that host excitations with restricted mobility.  I will discuss two different frameworks for formulating fracton physics.  First, I will show that certain gapless fracton phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose generators do not commute with spatial translations.  The mobility restrictions on particle worldlines are fully determined by the underlying symmetry algebra, and we may systematically construct effective field theories which at low energies reduce to known fractonic higher-rank gauge theories.  Following this, I will change gears and discuss how key aspects of fracton physics can also be reproduced within the geometric framework of double field theory (DFT).  I will argue that the restricted mobility and large degeneracy of quantum states can be attributed to the generalized geodesics and infinite-dimensional isometries present in non-Riemannian backgrounds of DFT.  These two systematic approaches to fracton phases enable the engineering of any desired mobility restrictions.  To conclude, I will comment on the possibility of a unified understanding of fractons from symmetry and geometry.

Talk 2: Testing O(D,D) string cosmology based on double field theory

The low-energy limit of string theory contains additional gravitational degrees of freedom, the B-field and dilaton, that are not present in general relativity.  Together with the metric, these three fields are naturally embedded in the O(D,D)-symmetric framework of double field theory (DFT).  Furthermore, extending the O(D,D) symmetry to additional matter fixes a modified minimal coupling in string frame and leads to a DFT version of Einstein's equations, in which the resulting DFT energy-momentum tensor is enhanced to include dilaton pressure and skew-symmetric contributions.  After reviewing the DFT formalism, I will explore its cosmological implications: I will describe how homogeneous and isotropic backgrounds can be characterized by two equation-of-state parameters, and I will present some analytic solutions that provide candidate models for bouncing cosmologies.  Then I will discuss recent progress toward testing O(D,D) cosmology, including implications for structure formation, luminosity distance measurements, and a possible non-Riemannian origin of the universe.

Talk 1: Holographic Approach to Quantum Chaos

One of the criteria for quantum chaos is the OTOC. We evaluate this in the bulk with the corresponding operators at the boundary in various geometries, and discuss the physical implications.

Talk 2: Higher Curvature Effects on PBH Formation

Higher Curvature terms usually appear in various gravity models beyond Einstein. Our goal is to understand the role of the higher curvature terms in primordial black hole (PBH) formation. We will approach this goal by studying the specific and simpler Einstein-dilaton-Gauss-Bonnet gravity theory. The key is understanding the Misner Equations in this higher-gravity theory. This presentation is based on work in progress.

Trilogy of quantum liquid : From dark matter to correlated electrons I, II

I will first review the idea of dark matter as Bose liquid as a mean field theory approach to dark matter distribution. Then I will talk about holographic mean field theory for the correlated electrons. Finally,  I will talk about the strange metal based on Yukawa-SYK model and the physical origin of the SYK. 

Beyond BMS: Carrollian Symmetries in Flat Holography

Null infinity naturally carries a Carrollian geometry, suggesting that the symmetry structure relevant for flat holography may extend beyond the standard BMS transformations. In this talk, I will discuss the canonical realization of the full set of local Carrollian transformations at three-dimensional null infinity, including Carrollian diffeomorphisms, Weyl transformations, and local Carroll boosts. Particular emphasis will be placed on the existence of two distinct Carroll-Weyl transformations: one that rescales the Carrollian volume form, and a second, volume-preserving transformation that acts independently on the clock and spatial structures. I will show that, while the first sector can be accommodated within three-dimensional Einstein gravity, the second is obstructed at the level of its canonical realization. I will then explain how this obstruction can be lifted by embedding the problem into three-dimensional conformal gravity. The resulting enlarged phase space provides the additional boundary degrees of freedom needed to realize the missing Carrollian transformations, yielding a bulk realization of an extended Carrollian symmetry structure at null infinity and offering a new perspective on the symmetry content of flat holography.

Dissipative Field Theories for Nambu-Goldstone Modes of Higher-Form Symmetries

Symmetry provides a powerful organizing principle for low-energy effective theories. Higher-form symmetries extend this idea to systems with extended charged objects, such as lines and surfaces. From this viewpoint, photons can be regarded as Nambu-Goldstone modes of a spontaneously broken U(1) one-form symmetry. In this talk, I will discuss how this symmetry-based picture can be extended to finite-temperature real-time dynamics. Using the Schwinger-Keldysh formalism, we construct dissipative effective field theories for Nambu-Goldstone modes of higher-form symmetries.

EM invariant theory of massless spin 2 from topological bulk

We will show how we can obtain a manifestly Lorentz and duality invariant theory of massless spin 2 from 5 dimensional BF theory.

Higher-form symmetries and d-wave superconductors from doped Mott insulators

Traditional frameworks classify phases of matter based on Landau’s paradigm of spontaneous symmetry breaking of conventional symmetries. Recent advancements, however, demonstrate that generalized higher-form symmetries and their spontaneous breaking serve as a powerful lens to characterize quantum entanglement structures, topological order, and emergent collective excitations. This modern viewpoint has successfully elucidated diverse quantum phenomena, ranging from emergent gauge fields in Maxwell theory to unbroken \(\mathbb{Z}_{3}\) two-form symmetries in dense QCD matter. It also provides physical constraints via the generalized Coleman-Mermin-Wagner theorem and radiative Coleman-Weinberg mechanisms.

Building upon these foundational concepts, this work focuses on the path to high-temperature cuprate superconductors via doping a Mott insulator, analyzed through the specific viewpoint of higher-form symmetries. By introducing slave bosons, the \(t\)-\(J\) model at a finite hole doping is mapped onto \(U(1)\) gauge theories. Following an Abelian duality transformation, the system is reformulated as a generalized BF theory, where the underlying continuous and discrete higher-form symmetries become manifest. Within this framework, we identify emergent higher-form symmetries in both \(s\)-wave and \(d\)-wave superconducting phases expected to realize from a doped Mott insulator. By systematically testing the existence of topological order through the spontaneous breaking of a discrete one-form symmetry, we demonstrate that this broken symmetry can persist to cause a potential topological phase transition inside the superconducting dome of high-\(T_{c}\) cuprates.

Holography and Renormalization: RG Flows and Emergent Spacetime

Holography is the proposal that a theory of semiclassical gravity in a bulk spacetime is equivalent to a non-gravitational field theory on its boundary. The renormalization group (RG) describes how a system's effective description changes as short-distance degrees of freedom are integrated out thus supplying a natural origin for the emergent bulk direction: flow of energy scale is geometrized into the extra dimension. In this talk, I will demonstrate the philosophy of holography-as-RG correspondence in a path-integral language (using functional techniques). I will first demonstrate how a Fokker-Planck-type functional RG equation for a probability distribution is solved by a holographic bulk action. In the semiclassical limit, its Hamilton-Jacobi form yields a generalized dual holography with RG beta-functions built into the bulk. Then I will describe two ongoing directions of work:

1. In AdS_3/CFT_2, integrating out a non-minimally coupled bulk scalar produces a higher-derivative gravity theory whose one-loop corrections reproduce non-planar (1/N) contributions to a deformed boundary CFT. This will essentially build up the holographic dictionary beyond leading order and give a systematic handle on 1/N corrections.

2. I will show how one can recast the holographic dual effective field theory as a functional RG within the Luttinger-Ward approach, and apply it to the SYK model. In particular, the RG-improved bulk action will indeed show the SL(2,R) symmetries of the leading part.

Restricted gravity: Lagrangian formalism and explicit solutions

It is well known that, by making the Abelian projection of Einstein’s theory, one can obtain restricted gravity, which is simpler than Einstein’s theory but describes the core dynamics of Einstein’s gravity. In this talk, we present the Lagrangian formalism of restricted gravity, which makes it a self-consistent field theory independent of Einstein’s theory. With this, we present interesting solutions of restricted gravity, in particular the gravitational cosmic string, the Bertotti Robinson spacetime, the axisymmetric pp-wave, and the conformally flat waves with flat wavefront. Moreover, we show that in restricted gravity the Rosen–Bondi gravitational plane wave could be described by two Maxwellian potentials. This could play an important role in quantum gravity. We discuss the physical implications of the restricted gravity.

Generating rotating spacetime by anholonomic frame transformation

Despite its numerous phenomenological successes, the inner working mechanism of the famous Newman-Janis algorithm remains an unresolved question in classical general relativity. In this talk, I will outline some of our recent understanding toward this end, which sheds light on some aspects of the Newman-Janis algorithm from an anholonomic frame transformation perspective. 

Non-relativistic QFT and spontaneous symmetry breaking 

In this talk we will readdress the spontaneous symmetry breaking of higher form symmetries in standard QFT in a rigours and systematic way, a la Weinberg. We extend this discussion to non-relativistic QFTs, specifically Galilean QFT. We discuss its consequences including counting of broken generators a d photonization in 3 dimensions.

Partition Functions in Chiral and Democratic Theories From a Generalized Symmetry Perspective

In this talk, I will review the construction of partition functions for chiral theories, emphasizing the role of self-dual fields in their quantum formulation and the role of the higher form symmetries. I will begin by outlining the key ingredients of the formalism, including the treatment of self-dual fields and the construction of consistent quantum partition functions. I will then show how these ideas naturally extend to democratic M-theory, leading to a consistent construction of its partition function.

Quantum Chaos and Krylov Complexity in Yukawa-SYK

We study many-body dynamics in a zero-dimensional Yukawa–SYK model, focusing on Krylov state complexity as a probe of interaction-driven dynamics. By constructing the Krylov basis through the Lanczos procedure, we characterise the spreading of an initially chosen state in Krylov space and examine how this spreading changes across the parameter regime connecting SYK(_2)- and SYK(_4)-like behaviour. We compare the Krylov complexity with conventional measures of spectral and wavefunction statistics, and find that it provides complementary information about the many-body dynamics.

SymTFT and entropic order parameters

In this talk, we will demonstrate that the symmetry topological field theory (SymTFT) construction, also known as topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken symmetries. In particular, the origin of the distinguishability of the vacua resulting from spontaneously broken non-invertible symmetries can be made manifest with an information-theoretic perspective, where certain operators in the SymTFT are excluded from observation. If time permits, we will look at several concrete examples.