arXiv subjects

Kartik Prabhu

Publications and source records attributed to Kartik Prabhu.

At least 19 recordsLinked to original sources

arXiv2026

Perturbative semiclassical entropy of dynamical black holes

We consider perturbative quantum gravity as a quantum field theory of linearized metric perturbation on an asymptotically flat spacetime with a bifurcate Killing horizon. We include the perturbative gravitational constraints into the algebra of observables restricted to the right half of the future horizon of the spacetime. We use the boundary charge, associated to the horizon Killing field, as an auxiliary "observer" degree of freedom. The observables "dressed" with the additional charge are invariant under the Killing symmetry and generate a Type-$\text{II}_{\infty}$ von Neumann factor. We compute the von Neumann entropy of the reduced density matrix of a classical-quantum coherent state constructed from the metric perturbations and the "observer wavefunction". This von Neumann entropy satisfies an analogue of the first law of thermodynamics. We further show that this entropy is related to Hollands-Wald-Zhang entropy of the (second order) perturbed dynamical black hole through the flux of perturbations through the horizon and future null infinity.

hep-th↗

arXiv2025

Voyager: An End-to-End Framework for Design-Space Exploration and Generation of DNN Accelerators

While deep neural networks (DNNs) have achieved state-of-the-art performance in fields from computer vision to natural language processing, efficiently running these computationally demanding models requires hardware accelerators. However, designing these accelerators is a time-consuming, labor-intensive process that does not scale well. While prior efforts have sought to automate DNN accelerator generation, they offer limited parameterization, cannot produce high-performance, tapeout-ready designs, provide limited support for datatypes and quantization schemes, and lack an integrated, end-to-end software compiler. This work proposes Voyager, a high-level synthesis (HLS)-based framework for design space exploration (DSE) and generation of DNN accelerators. Voyager overcomes the limitations of prior work by offering extensive configurability across technology nodes, clock frequencies, and scales, with customizable parameters such as number of processing elements, on-chip buffer sizes, and external memory bandwidth. Voyager supports a wider variety of datatypes and quantization schemes versus prior work, including both built-in floating-point, posit and integer formats, as well as user-defined formats with both per-tensor scaling and microscaling quantization. Voyager's PyTorch-based compiler efficiently maps networks end-to-end on the generated hardware, with support for quantization, fusion, and tiling. We evaluate Voyager on state-of-the-art vision and language models. Voyager enables fast DSE with full-dataset accuracy evaluation for datatypes and quantization schemes. Generated designs achieve a high utilization across models and scales, up to 99.8%, and outperform prior generators with up to 61% lower latency and 56% lower area. Compared to hand-optimized accelerators, Voyager achieves comparable performance, while offering much greater automation in design and workload mapping.

cs.AR↗

arXiv2025

Vacua and infrared radiation in de Sitter quantum field theory

We analyze the asymptotic behavior of quantum fields and perturbative quantum gravity in de Sitter space. We show that the necessary and sufficient condition for the existence of a de Sitter invariant vacuum state in the free theory is if the local field observables commute with the ``memory observable'' on any cosmological horizon. This criterion yields simple, gauge-invariant proofs of the existence of a de Sitter invariant vacuum for the (source-free) massive scalar field, electromagnetic field and linearized gravitational field. However, the massless, minimally coupled scalar does not satisfy this criterion and, consequently, there is no de Sitter invariant vacuum state. In this case, we construct the Hilbert space of normalizable states that have ``square integrable'' distributions in the memory and the conjugate constant mode. This Hilbert space has a unitary representation of the de Sitter symmetry group but no de Sitter invariant normalizable state. However even for free theories with a normalizable de Sitter invariant vacuum we show, by a simple example, that in the presence of a source a large number of infrared particles can be produced if the source interacts with the field for timescales much longer than the Hubble time. In the limit as the source persists forever it emits an infinite number of infrared particles.

hep-th↗

arXiv2024

Infrared finite scattering theory: Amplitudes and soft theorems

Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an out-state with memory. Scattering with any massless fields violates the standard assumption of asymptotic completeness -- that all "in" and "out" states lie in the standard (zero memory) Fock space -- and therefore leads to infrared (IR) divergences in the standard $S$-matrix amplitudes. In this paper we define an infrared finite scattering theory which assumes only (1) the existence of in/out algebras and (2) that Heisenberg evolution is an automorphism of these algebras. The resulting "superscattering" map $\$$ allows for transitions between different in/out memory states and agrees with the standard $S$-matrix when it is defined. We construct $\$$-amplitudes by defining (3) a "generalized asymptotic completeness" which accommodates states with memory in the space of asymptotic states and (4) a complete basis of improper states which generalize the usual $n$-particle momentum basis to account for states with memory. Using only general properties of $\$$, we prove an analog of the Weinberg soft theorems in quantum gravity and QED which imply that all $\$$-amplitudes are well-defined in the infrared. We comment on how one must generalize this framework to consider $\$$-amplitudes for theories with collinear divergences (e.g., massless QED and Yang-Mills theories).

hep-th↗

arXiv2024

Infrared finite scattering theory: Scattering states and representations of the BMS group

Any non-trivial scattering with any massless fields in four spacetime dimensions will generically produce an "out" state with memory which gives rise to infrared divergences in the standard $S$-matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the "Lorentz orbit" of a given memory and classify all "orbit space representations" that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincaré group with memory for more general quantum field theories.

hep-th↗

arXiv2024

BMS-supertranslation charges at the critical sets of null infinity

For asymptotically flat spacetimes, a conjecture by Strominger states that asymptotic BMS-supertranslations and their associated charges at past null infinity $\mathscr{I}^{-}$ can be related to those at future null infinity $\mathscr{I}^{+}$ via an antipodal map at spatial infinity $i^{0}$. We analyse the validity of this conjecture using Friedrich's formulation of spatial infinity, which gives rise to a regular initial value problem for the conformal field equations at spatial infinity. A central structure in this analysis is the cylinder at spatial infinity representing a blow-up of the standard spatial infinity point $i^{0}$ to a 2-sphere. The cylinder touches past and future null infinities $\mathscr{I}^{\pm}$ at the critical sets. We show that for a generic class of asymptotically Euclidean and regular initial data, BMS-supertranslation charges are not well-defined at the critical sets unless the initial data satisfies an extra regularity condition. We also show that given initial data that satisfy the regularity condition, BMS-supertranslation charges at the critical sets are fully determined by the initial data and that the relation between the charges at past null infinity and those at future null infinity directly follows from our regularity condition.

gr-qc↗

arXiv2023

Symmetries and charges of general relativity at null boundaries

We study general relativity at a null boundary using the covariant phase space formalism. We define a covariant phase space and compute the algebra of symmetries at the null boundary by considering the boundary-preserving diffeomorphisms that preserve this phase space. This algebra is the semi-direct sum of diffeomorphisms on the two sphere and a nonabelian algebra of supertranslations that has some similarities to supertranslations at null infinity. By using the general prescription developed by Wald and Zoupas, we derive the localized charges of this algebra at cross sections of the null surface as well as the associated fluxes. Our analysis is covariant and applies to general non-stationary null surfaces. We also derive the global charges that generate the symmetries for event horizons, and show that these obey the same algebra as the linearized diffeomorphisms, without any central extension. Our results show that supertranslations play an important role not just at null infinity but at all null boundaries, including non-stationary event horizons. They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.

hep-th↗

arXiv2023

Supergravity model of the Haldane-Rezayi fractional quantum Hall state

Supersymmetry and supergravity were invented in the 1970s to solve fundamental problems in high-energy physics. Even though neither of these ideas has yet been confirmed in high-energy and cosmology experiments, they have been beneficial in constructing numerous theoretical models, including superstring theory. Despite the absence of supersymmetry in particle physics, it can potentially emerge in exotic phases of strongly correlated condensed matter systems. In this paper, we propose a supergravity model that describes the low-energy physics of the Haldane-Rezayi state, a gapless quantum Hall state that occurs in a half-filled Landau level. We show that the corresponding edge modes of the Haldane-Rezayi state and the Girvin-MacDonald-Platzman algebra appear naturally in the supergravity model. Finally, we substantiate our theoretical findings with numerical exact diagonalization calculations that support the appearance of the emergent graviton and gravitino excitations in the Haldane-Rezayi state.

cond-mat.str-el↗

arXiv2022

DS6, Deformation-aware Semi-supervised Learning: Application to Small Vessel Segmentation with Noisy Training Data

Blood vessels of the brain provide the human brain with the required nutrients and oxygen. As a vulnerable part of the cerebral blood supply, pathology of small vessels can cause serious problems such as Cerebral Small Vessel Diseases (CSVD). It has also been shown that CSVD is related to neurodegeneration, such as Alzheimer's disease. With the advancement of 7 Tesla MRI systems, higher spatial image resolution can be achieved, enabling the depiction of very small vessels in the brain. Non-Deep Learning-based approaches for vessel segmentation, e.g., Frangi's vessel enhancement with subsequent thresholding, are capable of segmenting medium to large vessels but often fail to segment small vessels. The sensitivity of these methods to small vessels can be increased by extensive parameter tuning or by manual corrections, albeit making them time-consuming, laborious, and not feasible for larger datasets. This paper proposes a deep learning architecture to automatically segment small vessels in 7 Tesla 3D Time-of-Flight (ToF) Magnetic Resonance Angiography (MRA) data. The algorithm was trained and evaluated on a small imperfect semi-automatically segmented dataset of only 11 subjects; using six for training, two for validation, and three for testing. The deep learning model based on U-Net Multi-Scale Supervision was trained using the training subset and was made equivariant to elastic deformations in a self-supervised manner using deformation-aware learning to improve the generalisation performance. The proposed technique was evaluated quantitatively and qualitatively against the test set and achieved a Dice score of 80.44 $\pm$ 0.83. Furthermore, the result of the proposed method was compared against a selected manually segmented region (62.07 resultant Dice) and has shown a considerable improvement (18.98\%) with deformation-aware learning.

eess.IV↗

arXiv2022

Infrared Finite Scattering Theory in Quantum Field Theory and Quantum Gravity

Infrared (IR) divergences arise in scattering theory with massless fields and are manifestations of the memory effect. There is nothing singular about states with memory, but they do not lie in the standard Fock space. IR divergences are artifacts of trying to represent states with memory in the standard Fock space. For collider physics, one can impose an IR cutoff and calculate inclusive quantities. But, this approach cannot treat memory as a quantum observable and is highly unsatisfactory if one views the S-matrix as fundamental in QFT and quantum gravity, since the S-matrix is undefined. For a well-defined S-matrix, it is necessary to define in/out Hilbert spaces with memory. Such a construction was given by Faddeev and Kulish (FK) for QED. Their construction "dresses" momentum states of the charged particles by pairing them with memory states of the electromagnetic field to produce states of vanishing large gauge charges at spatial infinity. However, in massless QED, due to collinear divergences, the "dressing" has an infinite energy flux so these states are unphysical. In Yang-Mills theory the "soft particles" used for dressing also contribute to the current flux, invalidating the FK procedure. In quantum gravity, the analogous FK construction would attempt to produce a Hilbert space of eigenstates of supertranslation charges at spatial infinity. However, we prove that there are no eigenstates of supertranslation charges except the vacuum. Thus, the FK construction fails in quantum gravity. We investigate some alternatives to FK constructions but find that these also do not work. We believe that to treat scattering at a fundamental level in quantum gravity - as well as in massless QED and YM theory - it is necessary to take an algebraic viewpoint rather than shoehorn the in/out states into some fixed Hilbert space. We outline the framework of such an IR finite scattering theory.

hep-th↗

arXiv2022

Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity

We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity and satisfy an additional set of conditions which we lay out explicitly. Combined with earlier results on the matching of supertranslation charges, this shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacetimes, proving a relationship that was conjectured by Strominger. Assuming additional suitable conditions are satisfied at timelike infinities, this proves that the flux of all BMS charges is conserved in any classical gravitational scattering process in these spacetimes.

gr-qc↗

arXiv2022

The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity

We use the formalism developed by Wald and Zoupas to derive explicit covariant expressions for the charges and fluxes associated with the Bondi-Metzner-Sachs symmetries at null infinity in asymptotically flat spacetimes in vacuum general relativity. Our expressions hold in non-stationary regions of null infinity, are local and covariant, conformally-invariant, and are independent of the choice of foliation of null infinity and of the chosen extension of the symmetries away from null infinity. While similar expressions have appeared previously in the literature in Bondi-Sachs coordinates (to which we compare our own), such a choice of coordinates obscures these properties. Our covariant expressions can be used to obtain charge formulae in any choice of coordinates at null infinity. We also include detailed comparisons with other expressions for the charges and fluxes that have appeared in the literature: the Ashtekar-Streubel flux formula, the Komar formulae, and the linkage and twistor charge formulae. Such comparisons are easier to perform using our explicit expressions, instead of those which appear in the original work by Wald and Zoupas.

gr-qc↗

arXiv2022

A novel supersymmetric extension of BMS symmetries at null infinity

We show that we can combine the (complex, self-dual) BMS vector fields with the recently defined BMS twistors to obtain a new supersymmetric extension of the BMS symmetries at null infinity. We compare our construction to other supersymmetric extensions of the BMS algebra proposed in the context of supergravity. Unlike the standard constructions the anticommutator in our superalgebra generates all the BMS vector fields including the Lorentz transformations. We also show that there exists a projection from our BMS Lie superalgebra to the global subalgebra of the Neveu-Schwarz supersymmetries on a 2-sphere, which are commonly considered in string theory and 2-dimensional conformal field theory.

gr-qc↗

arXiv2022

A Full-Stack Search Technique for Domain Optimized Deep Learning Accelerators

The rapidly-changing deep learning landscape presents a unique opportunity for building inference accelerators optimized for specific datacenter-scale workloads. We propose Full-stack Accelerator Search Technique (FAST), a hardware accelerator search framework that defines a broad optimization environment covering key design decisions within the hardware-software stack, including hardware datapath, software scheduling, and compiler passes such as operation fusion and tensor padding. In this paper, we analyze bottlenecks in state-of-the-art vision and natural language processing (NLP) models, including EfficientNet and BERT, and use FAST to design accelerators capable of addressing these bottlenecks. FAST-generated accelerators optimized for single workloads improve Perf/TDP by 3.7x on average across all benchmarks compared to TPU-v3. A FAST-generated accelerator optimized for serving a suite of workloads improves Perf/TDP by 2.4x on average compared to TPU-v3. Our return on investment analysis shows that FAST-generated accelerators can potentially be practical for moderate-sized datacenter deployments.

cs.LG↗

arXiv2022

A twistorial description of BMS symmetries at null infinity

We describe a novel twistorial construction of the asymptotic BMS symmetries at null infinity for asymptotically flat spacetimes. We define BMS twistors as spinor solutions to some set of components of the usual spacetime twistor equation restricted to null infinity. The space of BMS twistors is infinite-dimensional. We show that given two BMS twistors their symmetric tensor product can be used to generate (complex) vector fields which are the infinitesimal BMS symmetries of null infinity. In this sense BMS twistors are "square roots" of BMS symmetries. We also show that these BMS twistor equations can be written a pair of covariant spinor-valued equations which are completely determined by the intrinsic universal structure of null infinity.

gr-qc↗

arXiv2020

BMS-like symmetries in cosmology

Null infinity in asymptotically flat spacetimes posses a rich mathematical structure; including the BMS group and the Bondi news tensor that allow one to study gravitational radiation rigorously. However, FLRW spacetimes are not asymptotically flat because their stress-energy tensor does not decay sufficiently fast and in fact diverges at null infinity. This class includes matter- and radiation-dominated FLRW spacetimes. We define a class of spacetimes whose structure at null infinity is similar to FLRW spacetimes: the stress-energy tensor is allowed to diverge and the conformal factor is not smooth at null infinity. Interestingly, for this larger class of spacetimes, the asymptotic symmetry algebra is similar to the BMS algebra but not isomorphic to it. In particular, the symmetry algebra is the semi-direct sum of supertranslations and the Lorentz algebra, but it does not have any preferred translation subalgebra. Future applications include studying gravitational radiation in FLRW the full nonlinear theory, including the cosmological memory effect, and also asymptotic charges in this framework.

gr-qc↗

arXiv2020

Asymptotic symmetries and charges at spatial infinity in general relativity

We analyze the asymptotic symmetries and their associated charges at spatial infinity in $4$-dimensional asymptotically-flat spacetimes. We use the covariant formalism of Ashtekar and Hansen where the asymptotic fields and symmetries live on the $3$-manifold of spatial directions at spatial infinity, represented by a timelike unit-hyperboloid (or de Sitter space). Using the covariant phase space formalism, we derive formulae for the charges corresponding to asymptotic supertranslations and Lorentz symmetries at spatial infinity. With the motivation of, eventually, proving that these charges match with those defined on null infinity -- as has been conjectured by Strominger -- we do not impose any restrictions on the choice of conformal factor in contrast to previous work on this problem. Since we work with a general conformal factor we expect that our charge expressions will be more suitable to prove the matching of the Lorentz charges at spatial infinity to those defined on null infinity, as has been recently shown for the supertranslation charges.

gr-qc↗

arXiv2020

Angular momentum at null infinity in Einstein-Maxwell theory

On Minkowski spacetime, the angular momentum flux through null infinity of Maxwell fields, computed using the stress-energy tensor, depends not only on the radiative degrees of freedom, but also on the Coulombic parts. However, the angular momentum also can be computed using other conserved currents associated with a Killing field, such as the Noether current and the canonical current. The flux computed using these latter two currents is purely radiative. A priori, it is not clear which of these is to be considered the true flux of angular momentum for Maxwell fields. This situation carries over to Maxwell fields on non-dynamical, asymptotically flat spacetimes for fluxes associated with the Lorentz symmetries in the asymptotic Bondi-Metzner-Sachs (BMS) algebra. We investigate this question of angular momentum flux in the full Einstein-Maxwell theory. Using the prescription of Wald and Zoupas, we compute the charges associated with any BMS symmetry on cross-sections of null infinity. The change of these charges along null infinity then provides a flux. For Lorentz symmetries, the Maxwell fields contribute an additional term, compared to the Wald-Zoupas charge in vacuum general relativity, to the charge on a cross-section. With this additional term, the flux associated with Lorentz symmetries, e.g., the angular momentum flux, is purely determined by the radiative degrees of freedom of the gravitational and Maxwell fields. In fact, the contribution to this flux by the Maxwell fields is given by the radiative Noether current flux and not by the stress-energy flux.

gr-qc↗