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Duality In Equations of Motion from Spacetime Dependent Lagrangians  [PDF]
Rajsekhar Bhattacharyya,Debashis Gangopadhyay
Physics , 1998,
Abstract: Starting from lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit spacetime dependence of the lagrangian. Poincare invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both abelian and nonabelian dualities. We illustrate how (1)Dirac string solution (2)Dirac quantisation condition (3)t'Hooft-Polyakov monopole solutions and (4)a procedure emerges for obtaining {\it new} classical solutions of Yang-Mills (Y-M) theory. Moreover, these results occur in a way that is strongly reminiscent of the {\it holographic principle}.
Spacetime Dependent Lagrangians and Weak-Strong Duality : Sine Gordon and Massive Thirring Models  [PDF]
Rajsekhar Bhattacharyya,Debashis Gangopadhyay
Physics , 2001, DOI: 10.1142/S021773230200631X
Abstract: The formalism of spacetime dependent lagrangians developed in Ref.1 is applied to the Sine Gordon and massive Thirring models.It is shown that the well-known equivalence of these models (in the context of weak-strong duality) can be understood in this approach from the same considerations as described in [1] for electromagnetic duality. A further new result is that all these can be naturally linked to the fact that the holographic principle has analogues at length scales much larger than quantum gravity. There is also the possibility of {\it noncommuting coodinates} residing on the boundaries. PACS: 11.15.-q: 11.10/Ef
On Electrogravity Duality  [PDF]
Naresh Dadhich
Physics , 1998, DOI: 10.1142/S0217732399000389
Abstract: By resolving the gravitational field into electric and magnetic parts, we define an electrogravity duality transformation and discover an interesting property of the field. Under the duality transformation a vacuum/flat spacetime maps into the original spacetime with a topological defect of global monopole/texture. The elctrogravity-duality is thus a topological defect generating process. It turns out that all black hole solutions possess dual solutions that imbibe a global monopole.
Spacetime Dependent Lagrangians and the Vacuum Expectation Value of the Higgs field  [PDF]
R. Bhattacharyya,Debashis Gangopadhyay
Physics , 2002,
Abstract: The spacetime dependent lagrangian formalism of references [1-2] is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field, viz. $\phi_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge). The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct D-brane actions. PACS:11.15.-q ; 11.27+d ; 11.10.Ef
Global monopoles and scalar fields as the electrogravity dual of Schwarzschild spacetime  [PDF]
Naresh Dadhich,Narayan Banerjee
Physics , 2000, DOI: 10.1142/S0217732301004376
Abstract: We prove that both global monopole and minimally coupled static zero mass scalar field are electrogravity dual of the Schwarzschild solution or flat space and they share the same equation of state, $T^0_0 - T^i_i = 0$. This property was however known for the global monopole spacetime while it is for the first time being established for the scalar field. In particular, it turns out that the Xanthopoulos - Zannias scalar field solution is dual to flat space.
Vacuum Expectation Value of the Higgs Field and Dyon Charge Quantisation from Spacetime Dependent Lagrangians  [PDF]
Rajsekhar Bhattacharyya,Debashis Gangopadhyay
Physics , 2002, DOI: 10.1142/S0217732303009289
Abstract: The spacetime dependent lagrangian formalism of references [1-2] is used to obtain is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field,{\it viz.} $\phi_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge).The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct $D$-brane actions. The formalism is also used to obtain the Deser-Gomberoff-Henneaux-Teitelboim results [10] for dyon charge quantisation in abelian $p$-form theories in dimensions $D=2(p+1)$ for both even and odd $p$. PACS: 11.15.-q,11.27.+d,11.10.Ef
Spacetime Duality and Superduality  [PDF]
C. P. Burgess,M. T. Grisaru,M. Kamela,M. E. Knutt-Wehlau,P. Page,F. Quevedo,M. Zebarjad
Physics , 1998, DOI: 10.1016/S0550-3213(98)00782-2
Abstract: We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global spacetime symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations are based on global internal symmetries. We illustrate these new duality transformations by dualizing several scalar and spin-half theories in 1+1 spacetime dimensions, involving nonsupersymmetric as well as (1,1) and (2,2) supersymmetric models. For (2,2) models the new duality transformations can interchange chiral and twisted-chiral multiplets.
On the tensor formulation of effective vector Lagrangians and duality transformations  [PDF]
Johan Bijnens,Elisabetta Pallante
Physics , 1995, DOI: 10.1142/S0217732396001107
Abstract: Using two different methods inspired by duality transformations we present the equivalence between effective Lagrangians for massive vector mesons using a vector field and an antisymmetric tensor field. This completes the list of explicit field transformations between the various effective Lagrangian methods to describe massive vector and axial vector mesons.
Electric-Magnetic Duality Invariant Lagrangians  [PDF]
Machiko Hatsuda,Kiyoshi Kamimura,Sayaka Sekiya
Physics , 1999, DOI: 10.1016/S0550-3213(99)00509-X
Abstract: We find general non-linear lagrangians of a U(1) field invariant under electric-magnetic duality. They are characterized by an arbitrary function and go to the Maxwell theory in the weak field limit. We give some explicit examples which are generalizations of the Born-Infeld theory.
Spacetime Supersymmetry and Duality in String Theory  [PDF]
Ramzi R. Khuri
Physics , 1995,
Abstract: I discuss the role of spacetime supersymmetry in the interplay between strong/weak coupling duality and target space duality in string theory which arises in string/string duality. This can be seen via the construction of string soliton solutions which in $N=4$ compactifications of heterotic string theory break more than $1/2$ of the spacetime supersymmetries but whose analogs in $N=2$ and $N=1$ compactifications break precisely $1/2$ of the spacetime supersymmetries. As a result, these solutions may be interpreted as stable solitons in the latter two cases, and correspond to Bogomol'nyi-saturated states in their respective spectra.
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