scholarly journals Renormalization of twisted Ramond fields in D1-D5 SCFT2

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
A. A. Lima ◽  
G. M. Sotkov ◽  
M. Stanishkov
Keyword(s):  
Short Distance ◽  
Bound States ◽  
Deformation Parameter ◽  
Structure Constant ◽  
Point Function ◽  
First Order ◽  
Structure Constants ◽  
Twist Operators ◽  
Marginal Deformation ◽  
Double Integrals

Abstract We explore the n-twisted Ramond sector of the deformed two-dimensional $$ \mathcal{N} $$ N = (4, 4) superconformal (T4)N/SN orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-N limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-N limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.

scholarly journals Dynamics of R-neutral Ramond fields in the D1-D5 SCFT

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
A. A. Lima ◽  
G. M. Sotkov ◽  
M. Stanishkov
Keyword(s):  
Correlation Function ◽  
Short Distance ◽  
Deformation Parameter ◽  
Analytic Form ◽  
Point Function ◽  
Genus Zero ◽  
Tensor Method ◽  
Anomalous Dimensions ◽  
Structure Constants ◽  
Marginal Deformation

Abstract We describe the effect of the marginal deformation of the $$ \mathcal{N} $$ N = (4, 4) super-conformal (T4)N/SN orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-N approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scaling dimensions of non-BPS fields appearing in the fusion. In the deformed CFT, at second order in the deformation parameter, the two-point function of the n-twisted Ramond fields is UV-divergent. We perform an appropriate regularization, together with a renormalization of the undeformed fields, obtaining finite, well-defined corrections to their two-point functions and their bare conformal weights, for n < N. The fields with maximal twist n = N remain protected from renormalization, with vanishing anomalous dimensions.

Three-point functions in N=4 supersymmetric Yang–Mills theory

2019 ◽  
pp. 449-500 ◽  
Author(s):  
Shota Komatsu
Keyword(s):  
Weak Coupling ◽  
Structure Constant ◽  
Point Function ◽  
Yang Mills ◽  
Structure Constants

This is a review of the integrability-based approach to the three-point function in N = 4 supersymmetric Yang–Mills theory. We first discuss the computation of the structure constant at weak coupling and show that the result can be recast as a sum over partitions of the rapidities of the magnons. We then introduce a non-perturbative framework, called the ‘hexagon approach’, and explain how one can use the symmetries and integrability to determine the structure constants.

scholarly journals BMS modular diaries: torus one-point function

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Arjun Bagchi ◽  
Poulami Nandi ◽  
Amartya Saha ◽  
Zodinmawia
Keyword(s):  
Cosmological Solution ◽  
Three Dimensions ◽  
Field Theories ◽  
Point Function ◽  
Asymptotic Structure ◽  
Highest Weight ◽  
Structure Constants ◽  
Flat Spacetimes ◽  
Geodesic Approximation ◽  
Highest Weight Representation

Abstract Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS) group are conjectured to be dual to asymptotically flat spacetimes in three dimensions. In this paper, we continue our investigations of the modular properties of these field theories. In particular, we focus on the BMS torus one-point function. We use two different methods to arrive at expressions for asymptotic structure constants for general states in the theory utilising modular properties of the torus one-point function. We then concentrate on the BMS highest weight representation, and derive a host of new results, the most important of which is the BMS torus block. In a particular limit of large weights, we derive the leading and sub-leading pieces of the BMS torus block, which we then use to rederive an expression for the asymptotic structure constants for BMS primaries. Finally, we perform a bulk computation of a probe scalar in the background of a flatspace cosmological solution based on the geodesic approximation to reproduce our field theoretic results.

Feshbach–Villars equation in a κ-Minkowski spacetime

2020 ◽  
Vol 35 (37) ◽  
pp. 2050307
Author(s):  
B. Hamil ◽  
M. Merad
Keyword(s):  
Experimental Data ◽  
Perturbation Theory ◽  
Deformation Parameter ◽  
Order Approximation ◽  
Minkowski Spacetime ◽  
Magnetic Interaction ◽  
Relativistic Limit ◽  
First Order ◽  
Klein Gordon ◽  
First Order Approximation

In this paper, by using the Dirac derivatives the Klein–Gordon (K-G) equation is determined in a [Formula: see text]-Minkowski spacetime. The dispersion relation and the first-order approximation case are deduced. The Feshbach–Villars (FV) equation is derived by applying the new linearization process to the time. We then study the effect of magnetic interaction on energies spectrum in a [Formula: see text]-Minkowski spacetime as an application, as a result we found that the energies spectrum are not symmetrical. We also study the case of hydrogen atom in non-relativistic limit by using perturbation theory. The upper bound of the [Formula: see text]-deformation parameter is evaluate, on the basis of the experimental data for [Formula: see text] transition frequency.

Reply to "A remark on Moore's new method of obtaining approximate solutions of the Dirac equation"

1981 ◽  
Vol 59 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
R. A. Moore ◽  
Sam Lee
Keyword(s):  
Dirac Equation ◽  
Structure Constant ◽  
Approximate Solutions ◽  
Wave Functions ◽  
Fine Structure Constant ◽  
Energy Calculation ◽  
Calculation Error ◽  
First Order ◽  
The One ◽  
The Individual

This work was written to clarify the use of a recently developed procedure to obtain approximate solutions of the one-particle Dirac equation directly and in response to a recent critique on its application to lowest order. The critique emphasized the fact that when the wave functions are determined only to zero order then a first order energy calculation contains significant errors of the order of α4, α being the fine structure constant, and a matrix element calculation error of order α2. Tomishima re-affirms that higher order solutions are required to obtain accuracy of these orders. In this work the hierarchy of equations occurring in the procedure is extended to first order and it is shown that exact solutions exist for hydrogen-like atoms. It is also shown that the energy in second order contains all of the contributions of order α4. In addition, we illustrate, in detail, that the procedure can be aplied in such a way as to isolate the individual components of the wave functions and energies as power series of α2. This analysis lays the basis for the determination of suitable numerical methods and hence for application to physical systems.

A FIVE DIMENSIONAL MODEL OF EFFECTIVE GRAVITATIONAL AND FINE-STRUCTURE CONSTANTS

2002 ◽  
Vol 17 (29) ◽  
pp. 4317-4323 ◽  
Author(s):  
J. P. MBELEK ◽  
M. LACHIÈZE-REY
Keyword(s):  
Fine Structure ◽  
Scalar Field ◽  
Gravitational Constant ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Five Dimensional Model ◽  
Bulk Scalar Field ◽  
Structure Constants ◽  
Good Agreement ◽  
Kaluza Klein

It is shown that the coupling of the Kaluza-Klein (KK) internal scalar field both to an external stabilizing bulk scalar field and to the geomagnetic field may explain the observed dispersion in laboratory measurements of the (effective) gravitational constant. Except the PTB 95 value, the predictions are found in good agreement with all of the experimental data. The cosmological variation of the fine-structure constant is also addressed.

scholarly journals DESCRIBING RECENTLY DISCOVERED NARROW STATES AS QUARKONIA USING A POTENTIAL MODEL

2005 ◽  
Vol 20 (16) ◽  
pp. 3774-3776 ◽  
Author(s):  
STANLEY F. RADFORD ◽  
WAYNE W. REPKO
Keyword(s):  
Long Range ◽  
Short Distance ◽  
Bound States ◽  
Potential Model ◽  
Linear Potential

We examine to what extent several recently discovered narrow resonances can be interpreted as conventional [Formula: see text] bound states describable using a potential model. In doing so, we use a semirelativistic approach, which includes both the v2/c2 and QCD one-loop corrections to the short distance potential and a long range linear potential together with its scalar and vector v2/c2 spin-dependent terms.

Theoretical Studies of the EPR g Factors and the Hyperfine Structure Constants of Cr3+ in MgS and SrS

2003 ◽  
Vol 58 (9-10) ◽  
pp. 503-506
Author(s):  
Shao-Yi Wu ◽  
Xiu-Ying Gao ◽  
Wei-Zi Yan
Keyword(s):  
Hyperfine Structure ◽  
Coupling Coefficient ◽  
Structure Constant ◽  
Theoretical Studies ◽  
Spin Orbit ◽  
Cluster Approach ◽  
Hyperfine Structure Constant ◽  
Structure Constants ◽  
G Factors

The EPR g factors and the hyperfine structure constant A factors for Cr3+ in MgS and SrS are theoretically studied by using the two-spin-orbit (S.O.)-coupling-coefficient formulas for a 3d3 ion in octahedra based on the cluster approach. In these formulas, both the contributions due to the S.O. coupling coefficient of the central 3d3 ion and that of ligands are taken into account. Based on these studies, the g and A factors of Cr3+ in both MgS and SrS are satisfactorily explained. The results are discussed.

scholarly journals Long and short distance behavior of the imaginary part of the heavy-quark potential

2022 ◽  
Vol 258 ◽  
pp. 04008
Author(s):  
Kirill Boguslavski ◽  
Babak Kasmaei ◽  
Michael Strickland
Keyword(s):  
Heavy Quark ◽  
Imaginary Part ◽  
Short Distance ◽  
Bound States ◽  
Yang Mills ◽  
Temporal Decay ◽  
Wide Range ◽  
Quark Potential ◽  
Heavy Quark Potential ◽  
Distance Behavior

The imaginary part of the effective heavy-quark potential can be related to the total in-medium decay width of of heavy quark-antiquark bound states. We extract the static limit of this quantity using classical-statistical simulations of the real-time Yang-Mills dynamics by measuring the temporal decay of Wilson loops. By performing the simulations on finer and larger lattices we are able to show that the nonperturbative results follow the same form as the perturbative ones. For large quark-antiquark separations, we quantify the magnitude of the non-perturbative long-range corrections to the imaginary part of the heavy-quark potential. We present our results for a wide range of temperatures, lattice spacings, and lattice volumes. We also extract approximations for the short-distance behavior of the classical potential.

scholarly journals Oseen's correction to stokes drag on axially symmetric arbitrary particle in transverse flow: A new approach

2014 ◽  
Vol 41 (3) ◽  
pp. 177-212
Author(s):  
Deepak Srivastava ◽  
Nirmal Srivastava
Keyword(s):  
Reynolds Number ◽  
General Expression ◽  
Deformation Parameter ◽  
Axial Flow ◽  
Transverse Flow ◽  
Axially Symmetric ◽  
New Approach ◽  
First Order ◽  
Stokes Drag ◽  
Axis Of Symmetry

In this paper, Oseen?s correction to Stokes drag experienced by axially symmetric particle placed in a uniform stream perpendicular to axis of symmetry(i.e. transverse flow) is obtained. For this, the linear relationship between axial and transverse Stokes drag is utilized to extend the Brenner?s formula for axial flow to transverse flow. General expression of Oseen?s correction to Stokes drag on axially symmetric particle placed in transverse flow is found to be new. This general expression is applied to some known axially symmetric bodies and obtained values of Oseen?s drag, up to first order terms in Reynolds number ?R?, are also claimed to be new and never exist in the literature. Numerical values of Oseen drag are also evaluated and their variations with respect to Reynolds number, eccentricity and deformation parameter are depicted in figures and compared with some known values. Some important applications are also highlighted.

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