Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

Relation between parity-even and parity-odd CFT correlation functions in three dimensions

In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as $$ {\mathcal{W}}^3 $$ W 3 and $$ {\mathcal{W}}^2\tilde{\mathcal{W}} $$ W 2 W ˜ . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.

Towards bootstrapping RG flows: sine-Gordon in AdS

The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS2, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.

The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry

The genus zero contribution to the four-point correlator $$ \left\langle {\mathcal{O}}_{p_1}{\mathcal{O}}_{p_2}{\mathcal{O}}_{p_3}{\mathcal{O}}_{p_4}\right\rangle $$ O p 1 O p 2 O p 3 O p 4 of half-BPS single-particle operators $$ {\mathcal{O}}_p $$ O p in $$ \mathcal{N} $$ N = 4 super Yang-Mills, at strong coupling, computes the Virasoro-Shapiro amplitude of closed superstrings in AdS5× S5. Combining Mellin space techniques, the large p limit, and data about the spectrum of two-particle operators at tree level in supergravity, we design a bootstrap algorithm which heavily constrains its α′ expansion. We use crossing symmetry, polynomiality in the Mellin variables and the large p limit to stratify the Virasoro-Shapiro amplitude away from the ten-dimensional flat space limit. Then we analyse the spectrum of exchanged two-particle operators at fixed order in the α′ expansion. We impose that the ten-dimensional spin of the spectrum visible at that order is bounded above in the same way as in the flat space amplitude. This constraint determines the Virasoro-Shapiro amplitude in AdS5× S5 up to a small number of ambiguities at each order. We compute it explicitly for (α′)5,6,7,8,9. As the order of α′ grows, the ten dimensional spin grows, and the set of visible two-particle operators opens up. Operators illuminated for the first time receive a string correction to their anomalous dimensions which is uniquely determined and lifts the residual degeneracy of tree level supergravity, due to ten-dimensional conformal symmetry. We encode the lifting of the residual degeneracy in a characteristic polynomial. This object carries information about all orders in α′. It is analytic in the quantum numbers, symmetric under an AdS5 ↔ S5 exchange, and it enjoys intriguing properties, which we explain and detail in various cases.

A Discrete Relativistic Spacetime Formalism for 1+1-QED With Continuum Limits

We build a quantum cellular automaton (QCA) which coincides with 1 + 1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with the gauge field on the links. The particles are massive fermions, and the evolution is exactly U(1) gauge-invariant. We show that, in the continuous-time discrete-space limit, the QCA converges to the Kogut-Susskind staggered version of 1 + 1 QED. We also show that, in the continuous spacetime limit and in the free one particle sector, it converges to the Dirac equation—a strong indication that the model remains accurate in the relativistic regime.

Notes on flat-space limit of AdS/CFT

Different frameworks exist to describe the flat-space limit of AdS/CFT, include momentum space, Mellin space, coordinate space, and partial-wave expansion. We explain the origin of momentum space as the smearing kernel in Poincare AdS, while the origin of latter three is the smearing kernel in global AdS. In Mellin space, we find a Mellin formula that unifies massless and massive flat-space limit, which can be transformed to coordinate space and partial-wave expansion. Furthermore, we also manage to transform momentum space to smearing kernel in global AdS, connecting all existed frameworks. Finally, we go beyond scalar and verify that $$ \left\langle VV\mathcal{O}\right\rangle $$ VV O maps to photon-photon-massive amplitudes.

A Satellite Town Development for Ambad MIDC Nashik

The concept of a satellite town is not a new one in India. Many efforts were made during the British era, and following independence, the Indian government made large-scale initiatives through policies, acts, and corporate partnerships. As is well acknowledged, India is experiencing rapid urbanization, resulting in city expansion and pseudo-urbanization due to land constraints. As a result, the satellite town concept must be implemented in order to develop new urban space, limit city boundaries, maximize land utilization, and raise the livability index of the city in order to attract investment. The study takes a multi-level approach, including a review of the literature, policies to better understand parameters, the identification of a new town site, and mitigation techniques. Following the identification of the area, a qualitative and quantitative study involving sampling, area-based observation, and public engagement was used to profile socioeconomic status. Chunchale village was chosen for the study, and it was discovered that this region has farm land on entire site. And can easily convert in NA land and use for proposal. In proposal most of the land will be proposed for residential as well as infrastructure purpose, as the project is dedicated to people working in Ambad MIDC for their occupation purpose. Based on area-based observation, the surrounding area appears to be ideal for commercial use too. It is suggested that a commercial hub be created near the rehab facility to stimulate the local economy and provide work opportunities for people. As land value rises and infilling area develops, such development also helps the surrounding area's development. Keywords: Satellite town, Redevelopment, Mix Land used, urban renewal policies, spatial planning, socio economic analysis

Views of Physical Education Teachers on Distance Education During the Covid-19 Pandemic Period: A Qualitative Study

This study was carried out in order to examine the opinions of physical education teachers about the remote (online) education of schools due to the Covid-19 epidemic in our country and in the world in recent years, and the remote teaching of physical education lessons in this process. Within the scope of this study, it was tried to determine the opinions of physical education teachers about the distance education process, the problems they encountered, the efficiency and adequacy of the lessons, the advantages and disadvantages of the process. The study was designed using a qualitative research method, and the study group was determined using the stratified sampling method. Study data were collected by the researcher by interview method. The analysis of the data was carried out using the content analysis method. According to the findings of the research, in the evaluations of the participants; It has been observed that the majority of them define distance education as virtual education, the majority of them express that it is important and necessary to teach physical education lessons in distance education, the biggest advantage in the process of teaching the lessons is the lack of time and space limit, and the disadvantage is that distance education cannot provide the same equality of opportunity for every student. At the end of the study, suggestions were given to make physical education lessons more efficient in the distance education process.

Anomaly Mining - Past, Present and Future

Anomaly mining is an important problem that finds numerous applications in various real world do- mains such as environmental monitoring, cybersecurity, finance, healthcare and medicine, to name a few. In this article, I focus on two areas, (1) point-cloud and (2) graph-based anomaly mining. I aim to present a broad view of each area, and discuss classes of main research problems, recent trends and future directions. I conclude with key take-aways and overarching open problems. Disclaimer. I try to provide an overview of past and recent trends in both areas within 4 pages. Undoubtedly, these are my personal view of the trends, which can be organized differently. For brevity, I omit all technical details and refer to corresponding papers. Again, due to space limit, it is not possible to include all (even most relevant) references, but a few representative examples.

The Effects of Inlet Blockage and Electrical Driving Mode on the Performance of a Needle-Ring Ionic Wind Pump

The thermal management of microelectronics is important because overheating can lead to various reliability issues. The most common thermal solution used in microelectronics is forced convection, which is usually initiated and sustained by an airflow generator, such as rotary fans. However, traditional rotary fans might not be appropriate for microelectronics due to the space limit. The form factor of an ionic wind pump can be small and, thus, could play a role in the thermal management of microelectronics. This paper presents how the performance of a needle-ring ionic wind pump responds to inlet blockage in different electrical driving modes (direct current), including the flow rate, the corona power, and the energy efficiency. The results show that the performance of small needle-ring ionic wind pumps is sensitive to neither the inlet blockage nor the electrical driving mode, making needle-ring ionic wind pumps a viable option for microelectronics. On the other hand, it is preferable to drive needle-ring ionic wind pumps by a constant current if consistent performance is desired.