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Jnanadeva Maharana

Publications and source records attributed to Jnanadeva Maharana.

At least 19 recordsLinked to original sources
arXiv2023

On Production of Excited Kaluza-Klein States in Large Radius Compactification Scenario

Production of exotic states at LHC is considered in the large radius compactification scenario. We envisage a five dimensional theory for a scalar field in five dimensional flat spacetime. It is compactified on a circle, $S^1$, with radius, $R$. The radius is assumed to be in TeV scale appealing to LRC hypothesis. The production of Kaluza-Klein states whose masses lie in the vicinity of TeV range is considered. Instead of appealing to any specific model, bounds on inelastic cross sections and near forward differental cross section are derived from the Lehmann-Symanzik-Zimmermann (LSZ) formulation. We consider decompactified theory should compactification radius be large enough to unravel the fifth spacial dimension in LHC energy scale. Bounds on cross sections are also derived for this scenario. We present bounds on inclusive cross sections for reactions like $a+b\rightarrow c+X$, X being unobserved states. We plot the bounds as a function of energy and propose that these bounds might be useful for search of exotic states in LHC experiments like ATLAS and CMS.

hep-th↗
arXiv2021

Causality, Crossing and Analyticity in Conformal Field Theories

Analyticity and crossing properties of four point function are investigated in conformal field theories in the frameworks of Wightman axioms. A Hermitian scalar conformal field, satisfying the Wightman axioms, is considered. The crucial role of microcausality in deriving analyticity domains is discussed and domains of analyticity are presented. A pair of permuted Wightman functions are envisaged. The crossing property is derived by appealing to the technique of analytic completion for the pair of permuted Wightman functions. The operator product expansion of a pair of scalar fields is studied and analyticity property of the matrix elements of composite fields, appearing in the operator product expansion, is investigated. An integral representation is presented for the commutator of composite fields where microcausality is a key ingredient. Three fundamental theorems of axiomatic local field theories; namely, PCT theorem, the theorem proving equivalence between PCT theorem and weak local commutativity and the edge-of-the-wedge theorem are invoked to derive a conformal bootstrap equation rigorously.

hep-th↗
arXiv2021

PCT Theorem, Wightman Axioms and Conformal Bootstrap

The axiomatic Wightman formulation for nonderivative conformal field theory is adopted to derive conformal bootstrap equation for the four point function. The equivalence between PCT theorem and {\it weak local commutativity}, due to Jost, play a very crucial role in axiomatic field theory. The theorem is suitably adopted for conformal field theory to derive the desired equations in CFT. We demonstrate that the two Wightman functions are analytic continuation of each other.

hep-th↗
arXiv2020

Analyticity Properties of Scattering Amplitude in Theories with Compactified Space Dimensions: The Proof of Dispersion Relations

The analyticity properties of the scattering amplitude for a massive scalar field is reviewed in this article where the spacetime geometry is $R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigated the analyticity of scattering amplitude in a nonrelativitstic potential model in three dimensions with an additional compact dimension. He showed that, under certain circumstances, the forward amplitude is nonanalytic. He argued that in high energy scattering if such a behaviour persists it would be in conflicts with the established results of quantum field theory and LHC might observe such behaviors. We envisage a real scalar massive field in flat Minkowski spacetime in five dimensions. The Kaluza-Klein (KK) compactification is implemented on a circle. The resulting four dimensional manifold is $R^{3,1}\otimes S^1$. The LSZ formalism is adopted to study the analyticity of the scattering amplitude. The nonforward dispersion relation is proved. In addition the Jin-Martin bound and an analog of the Froissart-Martin bound are proved. A novel proposal is presented to look for evidence of the large-radius-compactification scenario. A seemingly violation of Froissart-Martin bound at LHC energy might hint that an extra dimension might be decompactified. However, we find no evidence for violation of the bound in our analysis.

hep-th↗
arXiv2020

Froissart Bound, Diffraction Scattering of Hadrons and Scaling at Asymptotic Energies

The Froissart bound on the total cross section is subjected to test against very high energy data. We have found no clear evidence for its violation. The scaling property of differential cross section in the diffraction region is investigated. It exhibits scaling in the ISR, SPS, Tevatron and LHC energy domain which had hitherto remained unexplored. The slope of the diffraction peak is fitted and the data are tested against the rigorous bounds.

hep-ph↗
arXiv2020

Analyticity and Causality in Conformal Field Theory

We investigate analyticity properties of correlation functions in conformal field theories (CFT) in the Wightman formulation. The goal is to determine domain of holomorphy of permuted Wightman functions. We focus on crossing property of three-point functions. The domain of holomorphy of a pair of three-point functions is determined by appealing to Jost's theorem and by adopting the technique of analytic completion. This program paves the way to address the issue of crossing for the four-point functions on a rigorous footing.

hep-th↗
arXiv2020

Proof of dispersion relations for the amplitude in theories with a compactified space dimension

The analyticity properties of the scattering amplitude in the nonforward direction are investigated for a field theory in the manifold $\mathbb{R}^{3,1}\times S^1$. A scalar field theory of mass $m_0$ is considered in $D = 5$ Minkowski space to start with. Subsequently, one spatial dimension is compactified to a circle. The mass spectrum of the resulting theory is: (a) a massive scalar of mass, $m_0$, same as the original five dimensional theory and (b) a tower of massive Kaluza-Klein states. We derive nonforward dispersion relations for scattering of the excited Kaluza-Klein states in the Lehmann-Symanzik-Zimmermann formulation of the theory. In order to accomplish this object, first we generalize the Jost-Lehmann-Dyson theorem for a relativistic field theory with a compact spatial dimension. Next, we show the existence of the Lehmann-Martin ellipse inside which the partial wave expansion converges. It is proved that the scattering amplitude satisfies fixed-$t$ dispersion relations when $|t|$ lies within the Lehmann-Martin ellipse.

hep-th↗
arXiv2018

Analyticity Property of Scattering Amplitude in Theories with Compactified Space Dimensions

We consider a massive, neutral, scalar field theory of mass $m_0$ in a five dimensional flat spacetime. Subsequently, one spatial dimension is compactified on a circle, $S^1$, ofradius $R$. The resulting theory is defined in the manifold, $R^{3,1}\otimes S^1$. The mass spectrum is a state of lowest mass, $m_0$, and a tower of massive Kaluza-Klein states. The analyticity property of the elastic scattering amplitude is investigated in the Lehmann-Symanzik-Zimmermann (LSZ) formulation of this theory. In the context of nonrelativistic potential scattering, for the $R^3\otimes S^1$ spatial geometry, it was shown that the forward scattering amplitude does not satisfy analyticity properties in some cases for a class of potentials. If the same result is valid in relativistic quantum field theory then the consequences will be far reaching. We show that the forward elastic scattering amplitude of the theory, in the LSZ axiomatic approach, satisfies forward dispersion relations. The importance of the unitarity constraint on the S-matrix, is exhibited in displaying the properties of the absorptive part of the amplitude.

hep-th↗
arXiv2016

Analyticity Properties and Asymptotic Behavior of Scattering Amplitude in Higher Dimensional Theories

The properties of the high energy behavior of the scattering amplitude of massive, neutral and spinless particles in higher dimensional field theories are investigated. The axiomatic formulation of Lehmann, Symanzik and Zimmermann is adopted. The analyticity properties of the causal, the retarded and the advanced functions associated with the four point elastic amplitudes are studied. The analog of the Lehmann-Jost-Dyson representation is obtained in higher dimensional field theories. The generalized J-L-D representation is utilized to derive the t-plane analyticity property of the amplitude. The existence of an ellipse analogous to the Lehmann ellipse is demonstrated. Thus a fixed-t dispersion relation can be written down with finite number of subtractions due to the temperedness of the amplitudes. The domain of analyticity of scattering amplitude in $s$ and $t$ variables is extended by imposing unitarity constraints. A generalized version of Martin's theorem is derived to prove the existence of such a domain in D-dimensional field theories. It is shown that the amplitude can be expanded in a power series in t which converges for |t|<R; R being s-independent. The positivity properties of absorptive amplitudes are derived to prove the $t$-plane analyticity of amplitude. In the extended analyticity domain dispersion relations are written with two subtractions. The bound on the total cross section is derived from LSZ axioms without any extra ad hoc assumptions.

hep-th↗
arXiv2015

High Energy Scattering in Higher Dimensional Theories

The high energy behavior of scattering amplitudes in spacetime dimensions, $D>4$, is investigated. The bound on total cross sections, $σ_t \le Constant~(los s)^{D-2}$, $D\ge 4$ has been obtained in the past under usual assumptions. I derive new bound on scattering amplitudes in the region $|t|<T_0$, $t$ being momentum transfer squared. and $T_0$ is a constant. The existence of a zero-free region for the amplitude in complex t-plane, is proved. I prove stronger upper and lower bounds for the absorptive amplitude in the domain $0<t<T_0$.

math-ph↗
arXiv2013

T-duality and Scattering of Stringy States

We present a procedure for application of T-duality transformation on scattering amplitudes of closed bosonic stringy states. These states arise due to compactification of closed string to lower spacetime dimensions through dimensional reduction. The amplitude, in the first quantized formalism, is computed by introducing vertex operators. The amplitude is constructed by the standard prescription and the vertex operators are required to respect conformal invariance. Such vertex operators are constructed in the weak field approximation. Therefore, the vertex operators of the stringy states of our interest are to be defined accordingly. We propose a prescription to implement T-duality on the three point functions and N-point functions. We argue that it is possible to generate new amplitudes through the transformations on a given amplitude just as T-duality transformations can take us to a new set of string vacuum when acted upon an initial set. Explicit examples are given for three point and four point functions.

hep-th↗
arXiv2013

The Worldsheet Perspective of T-duality Symmetry in String Theory

The purpose of this article is to present a pedagogical review of T-dualityin in string theory. The evolution of the closed string is envisaged on the worldsheet in the presence of its massless excitations. The duality symmetry is studied when some of the spacial coordinates are compactified on d-dimensional torus, $T^d$. The known results are reviewed to elucidate that equations of motion for the compact coordinates are $O(d,d)$ covariant, $d$ being the number of compact directions. Next, the vertex operators of excited massive levels are considered in a simple compactification scheme. It is shown that the vertex operators for each massive level can be cast in a T-duality invariant form in such a case. Subsequently, the duality properties of superstring is investigated in the NSR formulation for the massless backgrounds such as graviton and antisymmetric tensor. The worldsheet superfield formulation is found to be very suitable for our purpose. The Hassan-Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields to be very suitable for our purpose. The Hassan-Sen compactification is adopted and it is shown that the worldsheet equations of motion for compact superfields are $O(d,d)$ covariant when the backgrounds are independent of superfields along compact directions. The vertex operators for excited levels are presented in the NS-NS sector and it is shown that they can be cast in T-duality invariant form for the case of Hassan-Sen compactification scheme. An illustrative example is presented to realize our proposal.

hep-th↗
arXiv2012

T-duality of NSR superstring: The worldsheet perspective

We formulate target space duality symmetry of NSR superstring from the perspectives of worldsheet. The worldsheet action is presented in the superspace formalism in the presence of massless backgrounds. We start from a ${\hat D}$-dimensional target space worldsheet action and compactify the theory on a d-dimensional torus, $T^d$. It is assumed that the backgrounds are independent of compact (super)coordinates. We adopt the formalism of our earlier work to introduce dual supercoordinates along compact directions and introduce the corresponding dual backgrounds. It is demonstrated that combined equations of motion of the two sets of coordinates can be expressed in a manifestly $O(d,d)$ covariant form analogous to the equations of motions for closed bosonic string derived by us. Furthermore, we show that the vertex operators associated with excited massive levels of NSR string can be expressed in an $O(d,d)$ invariant form generalizing earlier result for closed bosonic string.

hep-th↗
arXiv2011

Phenomenological implications of $S$-duality symmetry

It is proposed that $S$-duality is a fundamental symmetry of nature which is spontaneously broken. Axion and dilaton are identified with the doublet of the $S$-duality symmetry group $SL(2,\mathbbm{R})$. The symmetry is broken at a high scale corresponding to the experimentally estimated axion decay constant $f_χ$. The symmetry breaking mechanism is discussed in analogy with PCAC in pion physics. $S$-duality invariant interactions of fermions with axion and dilaton doublet are introduced. The symmetry breaking mechanism contributes negligibly small corrections to fermion masses in the QCD sector. Inspired by universality in string theory, the $S$-duality invariant interaction of the axion-dilaton doublet to QCD fermions is proposed to generalize to all fermions. Phenomenological consequences of this broken symmetry are explored.

hep-ph↗
arXiv2010

Duality Symmetry of String Theory: A Worldsheet Perspective

We study duality and local symmetries of closed bosonic string from the perspectives of worldsheet approach in the phase space path integral formalism. It is shown that the Ward identities reflecting the local symmetries associated with massless excitations such as graviton and antisymmetric tensor can be cast in a duality covariant form. It is shown how the manifestly O(d,d) invariant Hamiltonian can be obtained in the Hassan-Sen toroidal compactification scheme, d being the number of compact dimensions. It is proposed that massive excited states possess a T-duality symmetry for constant (tensor) backgrounds. This conjecture is verified for the first massive level.

hep-th↗
arXiv2010

Massive Stringy States and T-duality Symmetry

We present evidence for the target space duality symmetry associated with massive excited states of closed bosonic string. The evolution of string is considered in ${\hat D}$ spacetime dimensions; out of which d spacial dimensions are compactified on torus. The phase space Hamiltonian formulation is adopted to unveil the T-duality symmetry from the worldsheet perspective. The existence of this symmetry is verified for a few massive levels. A systematic procedure is presented to study T-duality symmetry of vertex operators for all massive levels of closed bosonic string. It is argued that all vertex operators corresponding to excited massive states can be cast in an O(d,d) invariant form where d is the number of compact dimensions.

hep-th↗
arXiv2005

NSR String in Ads_3 Backgrounds: Nonlocal Charges

We consider NSR superstring in AdS_3 X S_3 X R_4 background. The action is expressed in terms of the variables on the group manifolds SL(2,R) and SU(2) as 1+1 dimensional sigma models with Wess-Zumino terms, associated with AdS_3 and S_3 respectively. R_4 is flat Euclidean space. We show the existence of classical nonlocal conserved currents in the superspace formulation for the nonlinear sigma model with the WZ term in the context of NSR string. We propose Ward identities utilizing the existence of the nonlocal conserved currents.

hep-th↗