Null States Research Articles

On the non-perturbative bulk Hilbert space of JT gravity

What is the bulk Hilbert space of quantum gravity? In this paper, we resolve this problem in 2d JT gravity, both with and without matter, providing an explicit definition of a non-perturbative Hilbert space specified in terms of metric variables. The states are wavefunctions of the length and matter state, but with a non-trivial and highly degenerate inner product. We explicitly identify the null states, and discuss their importance for defining operators non-perturbatively. To highlight the power of the formalism we developed, we study the non-perturbative effects for two bulk linear operators that may serve as proxies for the experience of an observer falling into a two-sided black hole: one captures the length of an Einstein-Rosen bridge and the other captures the center-of-mass collision energy between two particles falling from opposite sides. We track the behavior of these operators up to times of order eSBH\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {e}^{S_{\ extrm{BH}}} $$\\end{document}, at which point the wavefunction spreads to the complete set of eigenstates of these operators. If these observables are indeed good proxies for the experience of an infalling observer, our results indicate an O(1) probability of detecting a firewall at late times that is self-averaging and universal.

Null states and time evolution in a toy model of black hole dynamics

Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of states eS in a gravitational system much smaller than the number of states eSp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {e}^{S_{\ extrm{p}}} $$\\end{document} predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involves N = O(eS) of the possible eSp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {e}^{S_{\ extrm{p}}} $$\\end{document} perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact for N ≪ eS (in which case no quantum extremal surfaces can arise). In particular, even for small N, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimension D ≪ eS. We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.

Impact of Home Assignment on the Achievement of Students in Makawanpur District, Nepal

The main goal of the study is to analyze the impact of home assignment on the achievement of students. The null hypothesis states there is no association between practices of home assignment and the achievement of the students. The study was guided by Achievement Goal Theory of Nicholls as well as descriptive and analytical research design was applied. At the same time, the cross-sectional data collection method was administered. The study was carried out among 386 students of 14 sampled schools of Makawanpur district, Nepal 2024 AD. The students were selected with the stratified random sampling method. The study shows that the students of educated parents spent less time in doing home assignment as compared with the students of illiterate parents. The parental support seems to have positive result on doing home assignment of the students. The location of school and students did not have any effect on doing home assignment. The result shows that there was the positive impact of home assignment on the achievement of the students and statistically, there significant association (p=0.022≤ 0.05) between home assignment and the achievement of students. Home assignment for both the students and parents is a burden. There was a debate on home assignment that it harmed the mental health of the children, at the same time some studies claimed that it had a positive impact on the achievement of the students if administered effectively. The study also emphasized the importance of home assignment for the better achievement of the student in school life. The study helps educational institutions to form a strategic plan and develop the model of home assignment that enhance the achievement of students.

All OPEs invariant under the infinite symmetry algebra for gluons on the celestial sphere

S algebra is an infinite-dimensional Lie algebra, which is known to be the symmetry algebra of some gauge theories. It is a “colored version” of the w1+∞. In this paper, we write down all possible S-invariant (celestial) operator product expansions between two positive-helicity outgoing gluons and also find the Knizhnik-Zamolodchikov type null states for these theories. Our analysis hints at the existence of an infinite number of S-invariant gauge theories which include the (tree-level) maximally helicity-violating sector and the self-dual Yang-Mills theory. Published by the American Physical Society 2024

Framed DDF operators and the general solution to Virasoro constraints

We define the framed DDF operators by introducing the concept of local frames in the usual formulation of DDF operators. In doing so it is possible to completely decouple the DDF operators from the associated tachyon and show that they are good zero-dimensional conformal operators. These framed DDFs allow for an explicit covariant formulation of the general solution of the Virasoro constraints both on-shell and off-shell which depends on a unique set of tangent space lightcone polarizations. This is possible since the frame allows us to embed the SO(D-2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SO(D-2)$$\\end{document} lightcone physical polarizations into the SO(1,D-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SO(1,D-1)$$\\end{document} covariant ones in the most general way. The solution to the Virasoro constraints is not in the gauge that is usually used since the states obtained from DDF operators are generically the sum of terms which are partially transverse due to the presence of a projector but not traceless and terms which are partially traceless but not transverse. We then show that different embeddings are connected by states generated by improved Brower operators both on shell and off shell. Brower states are null on-shell and equivalent to BRST exact states. Therefore on shell one embedding is sufficient to compute all amplitudes except the ones with vanishing momentum. Off-shell a change of frame cannot be obtained by null states but only by Brower states. Improved Brower operators generate a gauge invariance associated with local frame rotations, which replaces the usual gauge invariance generated by Virasoro operators or BRST. To check the identification, we verify the matching of the expectation value of the second Casimir of the Poincaré group for some lightcone states with the corresponding covariant states built using the framed DDFs.

The black hole interior from non-isometric codes and complexity

Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of “non-isometric codes protected by computational complexity”. We show that many previous ideas, such as the existence of a large number of “null states”, a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, “state-dependent/state-specific” operator reconstruction, and the “simple entropy” approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.

Investigation of Nulling and Subpulse-drifting Properties of PSR J1649+2533 with FAST

We report the nulling and subpulse-drifting properties of PSR J1649+2533 with observations of the Five-hundred-meter Aperture Spherical Radio Telescope (FAST). The FAST observations reveal that the nulling fraction of this pulsar is about 20.9% ± 0.8% at 1250 MHz. The statistical study of the durations of the nulling and burst states shows that the burst states can persist for extended pulse periods, exceeding 100 periods in some cases, while the shortest lasts only a few pulse periods. The null states have a much shorter duration, with a maximum duration of less than 30 pulse periods. A comparative study between the pulse profiles of the first active pulse (FAP) and the last active pulse (LAP) shows that the pulse profiles of LAPs are stronger and wider than those of FAPs. An analysis of the two-dimensional fluctuation spectrum for the single-pulse stack indicates that the pulsar exhibits clear amplitude modulation and subpulse drifting. The periods are a P 3 = 2.5 ± 0.1 spin period and P 2 = 17.°0 ± 0.°5 at 1250 MHz, respectively. In addition, the multiband investigation shows that P 2 seems to increase with the increase of the observing frequency, i.e., P 2 ∝ ν 0.8±0.1. This seems to be caused by the increasing pulse-profile width with the frequency. The high-sensitivity FAST observations will enable a detailed understanding of the emission of this pulsar and provide important clues for theoretical studies of the radiation mechanism.

Solving anharmonic oscillator with null states: Hamiltonian bootstrap and Dyson-Schwinger equations

Solving anharmonic oscillator with null states: Hamiltonian bootstrap and Dyson-Schwinger equations

Horizon strings as 3D black hole microstates

We propose that 3d black holes are an ensemble of tensionless null string states. These microstates typically have non-zero winding. We evaluate their partition function in the limit of large excitation numbers and show that their combinatorics reproduces the Bekenstein-Hawking entropy and its semiclassical logarithmic corrections.

Taming Dyson-Schwinger Equations with Null States.

In quantum field theory, the Dyson-Schwinger equations are an infinite set of coupled equations relating n-point Green's functions in a self-consistent manner. They have found important applications in nonperturbative studies, ranging from quantum chromodynamics and hadron physics to strongly correlated electron systems. However, they are notoriously formidable to solve. One of the main obstacles is that a finite truncation of the infinite system is underdetermined. Recently, Bender etal. [Phys. Rev. Lett. 130, 101602 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.101602] proposed to make use of the large-n asymptotic behaviors and successfully obtained accurate results in D=0 spacetime. At higher D, it seems more difficult to deduce the large-n behaviors. In this Letter, we propose another avenue in light of the null bootstrap. The underdetermined system is solved by imposing the null state condition. This approach can be extended to D>0 more readily. As concrete examples, we show that the cases of D=0 and D=1 indeed converge to the exact results for several Hermitian and non-Hermitian theories of the gϕ^{n} type, including the complex solutions.

An infinite family of w1+∞ invariant theories on the celestial sphere

In this note we determine the graviton-graviton OPE and the null states in any w1+∞ symmetric theory on the celestial sphere. Our analysis shows that there exists a discrete infinite family of such theories. The MHV-sector and the quantum self dual gravity are two members of this infinite family. Although the Bulk Lagrangian description of this family of theories is not currently known to us, the graviton scattering amplitudes in these theories are heavily constrained due to the existence of null states. Presumably they are exactly solvable in the same way as the minimal models of 2-D CFT.

Wormholes, geons, and the illusion of the tensor product

In this paper I argue that the Hilbert space of states of a holographic, traversable wormhole does not factorize into the tensor product of the boundary Hilbert spaces. After presenting the general argument I analyze two examples: the scalar sectors of the BTZ geon and the AdS2 eternal wormhole. Utilizing real-time holography I derive the Hilbert spaces, identify the dual states and evaluate correlation functions. I show that the number of peculiarities associated with the wormhole and black hole physics emerges once the factorization is a priori assumed. This includes null states and null operators, highly entangled vacuum states and the cross-boundary interactions all emerging as avatars of non-factorization.

A strategy for improving the SHEPWM commutation speed of CSI through hybrid switches

High-power current source inverters (CSI) usually operate at a low switching frequency to reduce switching loss. To suppress low-order harmonics and simplify filter design, the selective harmonic elimination pulse width modulation (SHEPWM) technique is a feasible common modulation strategy in industrial applications. This paper proposes an operational strategy that uses an H7 current source inverter (H7-CSI) with hybrid switches to perform the SHEPWM technique. On the basis of retaining the conventional H6 inverter bridge, the commutation speed of the CSI is improved by an additional shunt-connected high-performance power switch. The proposed scheme solves the problem that the CSIs built with low-speed switches (such as GTOs) may have difficulty for implementing the setting pulse widths of null states, while further reducing the switching losses at an acceptable cost. In addition, mitigating the influence of overlap-time by optimizing the driving signal of the H6 converter bridge. Finally, simulation and experiments have verified the effectiveness of the proposed CSI scheme.

Hadamard states on spherically symmetric characteristic surfaces, the semi-classical Einstein equations and the Hawking effect

We investigate quasi-free Hadamard states defined via characteristic initial data on null cones centred at the axis of symmetry in spherically symmetric space-times. We characterize the necessary singular behaviour of null boundary two-point functions such that one can define non-linear observables at this null boundary and give formulas for the calculation of these observables. These results extend earlier characterizations of null boundary states defining Hadamard states in the bulk of the null cone. As an application of our derived formulas, we consider their implications for the semi-classical Einstein equations and calculate the vacuum polarization associated with Hawking radiation near a collapsing body.

Efficacy of vanadium in the treatment of anaemia in teenage group

According to WHO, Anaemia is a condition in which the number of red blood cells is insufficient to meet the body’s physiological need. Specific physiological need may vary with a person’s age, gender and residential elevation above sea altitude) smocking behavior and different stages of pregnancy; iron deficiency is thought to be the most common cause of anaemia globally, but nutritional deficiency include folate, vitamin B12 and vitamin A, acute and chronic inflammation, Homoeopathy has good remedies to see that the necessary elements are properly absorbed by the body and assimilation is corrected thereby tackling anaemia 1 and this way even the supplements are put to good use. If anaemia treated properly which is effective and inexpensive can reduce the statistics of overall death rates, maternal haemorrhage, reduced school performance and lowered productivity and thereby bring a dream into reality?Aim and objectives1.To study the impact of anaemia among teenagers.2.To study the effect of vanadium 6c potency on anaemic teenagers.An awareness class was conducted for students in a undergraduate institution and some of them are randomly selected for screening then selected 30 students who had haemoglobin less than 12g/dl for the study. The study was conducted for two months as per the guidelines of CCRH Delhi. In the first month all the subjects receive placebo with a specific dietary recommendations to improve haemoglobin level and haemoglobin level was estimated at an interval of fifteen days. In the second month all subjects received vanadium 6c potency (Four pills daily morning before food) and hemoglobin level was estimated at an interval of fifteen days. After the two months systematics study, a statistical analysis done with the help of qualified statistician. The null hypothesis states that vanadium metallicum does not have any effect on anaemia Observation and results: If p

On Galilean conformal bootstrap. Part II. ξ = 0 sector

In this work, we continue our work on two dimensional Galilean conformal field theory (GCFT2). Our previous work (2011.11092) focused on the ξ ≠ 0 sector, here we investigate the more subtle ξ = 0 sector to complete the discussion. The case ξ = 0 is degenerate since there emerge interesting null states in a general ξ = 0 boost multiplet. We specify these null states and work out the resulting selection rules. Then, we compute the ξ = 0 global GCA blocks and find that they can be written as a linear combination of several building blocks, each of which can be obtained from a sl(2, ℝ) Casimir equation. These building blocks allow us to give an Euclidean inversion formula as well. As a consistency check, we study 4-point functions of certain vertex operators in the BMS free scalar theory. In this case, the ξ = 0 sector is the only allowable sector in the propagating channel. We find that the direct expansion of the 4-point function reproduces the global GCA block and is consistent with the inversion formula.

The Impact of Creative Climate Dimensions on Individual Innovation Behaviour

Abstract The purpose of the study was to examine the impact of creative climate dimensions on individual innovation behaviour. Data were collected from 249 randomly selected respondents for 2021 using a survey questionnaire. Statistical analyses were assessed using, a statistical package for social science (SPSS version 22); Descriptive analysis was done for categorical variables by using frequency and percentage, and Logistic regression analysis was done at the ordinal level to determine the relationship between creative climate and individual innovation behaviour. A descriptive study was organized. The results were drawn based on empirical data collected by university staff. From the results, it can be concluded that the six independent variables under study sufficiently influence individual innovation behaviour. The model is statistically significant, as indicated by the chi-square value (66.066) since the p-value is less than 0.000. As a result, we conclude that the dependent variable and independent factors have a very strong association. In addition, the model Parallel line test is 0.077, (The null hypothesis states that the location parameters (slope coefficients) are the same across response categories.) this test indicates that we have not violated the assumption. Keywords: creative climate dimensions, individual innovation behaviour, ordered logit model, Erbil Polytechnic University, Soran University.

The Effectiveness of Promotional Tools in Making Covid-19 Vaccination a Success: Hypothesis Testing Methods for Changing Cochran's Version

This study aims to examine the effectiveness of promotional tools in the success of the Covid-19 vaccination. In this study, the approach used was quantitative. The quantitative approach method uses hypothesis testing on the Cochran version change. The hypothesis testing method against the Cochran change test was applied to more than two groups of data samples on a nominal value scale or dichotomous ordinal. Basically the testing of this hypothesis is carried out to ensure the presence or absence of significant differences between a number of pairs of frequencies or proportions. The conclusion of this study is a Q value of 3,578, a Q value smaller than the chi-square value in the table of 7.815. Because the Q value is smaller than the chi-square value in the table, the null hypothesis states that the four promotional tools in order to make the Covid-19 vaccination program a success do not have a significant difference in effectiveness. Under these conditions, television, radio, newspapers, and social media have the same level of effectiveness in supporting the promotion of the success of the Covid-19 vaccination program in Indonesia.

Surface defects, flavored modular differential equations, and modularity

Every 4D $\mathcal{N}=2$ superconformal field theory $\mathcal{T}$ corresponds to an associated vertex operator algebra $\mathbb{V}(\mathcal{T})$, which is in general nonrational with a more involved representation theory. Null states in $\mathbb{V}(\mathcal{T})$ can give rise to nontrivial flavored modular differential equations, which must be satisfied by the refined/flavored character of all the $\mathbb{V}(\mathcal{T})$ modules. Taking some ${A}_{1}$ theories ${\mathcal{T}}_{g,n}$ of class $\mathcal{S}$ as examples, we construct the flavored modular differential equations satisfied by the Schur index. We show that three types of surface defect indices give rise to common solutions to these differential equations and therefore are sources of $\mathbb{V}(\mathcal{T})$-module characters. These equations transform almost covariantly under modular transformations, ensuring the presence of logarithmic solutions which may correspond to characters of logarithmic modules.

Alpha states demystified — towards microscopic models of AdS2 holography

We continue our study of factorizing theories of dilaton gravity, characterized by a universal bilocal interaction. All such factorizing theories can be shown to have discrete spectra, distinguished only by their local dilaton potentials. We show how such theories can be used to construct all alpha-states in the Hilbert space of baby universes of ordinary JT gravity. Large classes of these theories with different local potentials are found to be non-perturbatively equivalent and have identical discrete spectra. This is a concrete example of how different bulk descriptions can give rise to the same boundary theory. Such equivalences manifest themselves as null states, which have to be quotiented out in order to construct a proper baby universe Hilbert space. Our results also allow us to revisit the mechanism discussed by Coleman, Giddings and Strominger and concretely link ensemble averaging to the appearance or disappearance of spacetime wormholes.We then investigate JT gravity deformed only by the universal bilocal interaction. In this theory, the only terms that do not cancel in a topological expansion are disks, which capture perturbative fluctuations around a two-dimensional black hole saddle. We find that this theory of black holes has an evenly spaced spectrum, instead of a quantum chaotic one. We present a dual quantum mechanical system with exactly the same discrete spectrum, and propose that this is an example of a new holographic duality between a two-dimensional theory of quantum gravity and a conventional quantum mechanics.