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We provide a unique and novel extension of da Costa's calculation of a quantum mechanically constrained particle by analyzing the perturbative back reaction of the quantum confined particle's eigenstates and spectra upon the geometry of the curved surface itself. We do this by first formulating a two dimensional action principle of the quantum constrained particle, which upon wave function variation reproduces Schr\"odinger's equation including da Costa's surface curvature induced potentials. Given this action principle, we vary its functional with respect to the embedded two dimensional inverse-metric to obtain the respective geometrodynamical Einstein equation. We solve this resulting Einstein equation perturbatively by first solving the da Costa's Schr\"odinger equation to obtain an initial eigensystem, which is used as initial-input data for a perturbed metric inserted into the derived Einstein equation. As a proof of concept, we perform this calculation on a two-sphere and show its first iterative perturbed shape. We also include the back reaction of a constant external magnetic field in a separate calculation. The geometrodynamical analysis is performed within a two dimensional dilation gravity analog, due to several computational advantages., Comment: 9 pages, 15 figures

In this work, we provide a thorough analysis of energy extraction via magnetic reconnection, a novel mechanism recently proposed by Comisso and Asenjo, for a Kerr-Newman black hole immersed in a perfect fluid dark matter (PFDM) background. Our studies focus on the impact of black hole spin $a$, electric charge $Q$ and PFDM parameter $\lambda$ on the horizons, ecoregions and circular geodesics at the equatorial plane of this black hole, and how they further influence the reconnection efficiency and energy extraction rate. Our results show that the size of ergoregion does not vary monotonically with increasing dark matter parameters $\lambda$, but it can significantly increase at faster spins ($a>0.8$) as the dark matter parameter $\lambda$ decreases, given the electric charge stays within $Q\in [0.2,0.5]$. We identify the optimal conditions for the combination of $a$, $Q$ and $\lambda$ that enable efficient energy extraction even when the black hole is not rapidly spinning. The Kerr-Newman black hole in PFDM allows for achieving high energy extraction rates comparable to those of most previously studied rotating black holes, which typically require near-extremal spin to reach similar efficiency levels., Comment: 11 pages, 7 figures

In this paper we study black hole entropy universality within the Conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in Conformal Weyl gravity via both the N\"other current method and Wald's entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to Conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case we couple the conformal Weyl gravity field equations to a near horizon (linear) $U(1)$ gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However despite non-universality, the respective black hole entropies are in congruence with Wald's entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call $\gamma$ and relating to the Weyl anomaly coefficient. The construction follows an $AdS_2/CFT_1$ correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work., Comment: 21 pages, no figures. References added. Minor revisions and edits based upon comments and feedback

In this paper we study black hole entropy universality within the Conformal Weyl gravity paradigm. We do this by first computing the entropy of specific vacuum and non-vacuum solutions, previously unexplored in Conformal Weyl gravity via both the N\"other current method and Wald's entropy formula. For the vacuum case, we explore the near horizon near extremal Kerr metric, which is also a vacuum solution to Conformal Weyl gravity and not previously studied in this setting. For the non-vacuum case we couple the conformal Weyl gravity field equations to a near horizon (linear) $U(1)$ gauge potential and analyze the respective found solutions. We highlight the non-universality of black hole entropy between our studied black hole solutions of varying symmetries. However despite non-universality, the respective black hole entropies are in congruence with Wald's entropy formula for the specific gravity theory. Finally and despite non-universality, we comment on the construction of a near horizon CFT dual to one of our unique non-vacuum solutions. Due to the non-universality, we must introduce a parameter (similarly to entropy calculations in LQG) which we also call $\gamma$ and relating to the Weyl anomaly coefficient. The construction follows an $AdS_2/CFT_1$ correspondence in the near horizon, which enables the computation of the full asymptotic symmetry group of the chosen non-vacuum conformal Weyl black hole and its near horizon quantum CFT dual. We conclude with a discussion and outlook for future work., Comment: 21 pages, no figures. References added. Minor revisions and edits based upon comments and feedback

Background: Porphyromonas gingivalis (P. gingivalis) and its gingipain virulence factors have been identified as pathogenic effectors in Alzheimer's disease (AD). In a recent study we demonstrated the presence of gingipains in over 90% of postmortem AD brains, with gingipains localizing to the cytoplasm of neurons. However, infection of neurons by P. gingivalis has not been previously reported. Objective: To demonstrate intraneuronal P. gingivalis and gingipain expression in vitro after infecting neurons derived from human inducible pluripotent stem cells (iPSC) with P. gingivalis for 24, 48, and 72 h. Methods: Infection was characterized by transmission electron microscopy, confocal microscopy, and bacterial colony forming unit assays. Gingipain expression was monitored by immunofluorescence and RT-qPCR, and protease activity monitored with activity-based probes. Neurodegenerative endpoints were assessed by immunofluorescence, western blot, and ELISA. Results: Neurons survived the initial infection and showed time dependent, infection induced cell death. P. gingivalis was found free in the cytoplasm or in lysosomes. Infected neurons displayed an accumulation of autophagic vacuoles and multivesicular bodies. Tau protein was strongly degraded, and phosphorylation increased at T231. Over time, the density of presynaptic boutons was decreased. Conclusion: P. gingivalis can invade and persist in mature neurons. Infected neurons display signs of AD-like neuropathology including the accumulation of autophagic vacuoles and multivesicular bodies, cytoskeleton disruption, an increase in phospho-tau/tau ratio, and synapse loss. Infection of iPSC-derived mature neurons by P. gingivalis provides a novel model system to study the cellular mechanisms leading to AD and to investigate the potential of new therapeutic approaches.

Background: Porphyromonas gingivalis (P. gingivalis) and its gingipain virulence factors have been identified as pathogenic effectors in Alzheimer's disease (AD). In a recent study we demonstrated the presence of gingipains in over 90% of postmortem AD brains, with gingipains localizing to the cytoplasm of neurons. However, infection of neurons by P. gingivalis has not been previously reported. Objective: To demonstrate intraneuronal P. gingivalis and gingipain expression in vitro after infecting neurons derived from human inducible pluripotent stem cells (iPSC) with P. gingivalis for 24, 48, and 72 h. Methods: Infection was characterized by transmission electron microscopy, confocal microscopy, and bacterial colony forming unit assays. Gingipain expression was monitored by immunofluorescence and RT-qPCR, and protease activity monitored with activity-based probes. Neurodegenerative endpoints were assessed by immunofluorescence, western blot, and ELISA. Results: Neurons survived the initial infection and showed time dependent, infection induced cell death. P. gingivalis was found free in the cytoplasm or in lysosomes. Infected neurons displayed an accumulation of autophagic vacuoles and multivesicular bodies. Tau protein was strongly degraded, and phosphorylation increased at T231. Over time, the density of presynaptic boutons was decreased. Conclusion: P. gingivalis can invade and persist in mature neurons. Infected neurons display signs of AD-like neuropathology including the accumulation of autophagic vacuoles and multivesicular bodies, cytoskeleton disruption, an increase in phospho-tau/tau ratio, and synapse loss. Infection of iPSC-derived mature neurons by P. gingivalis provides a novel model system to study the cellular mechanisms leading to AD and to investigate the potential of new therapeutic approaches.

Background: Porphyromonas gingivalis (P. gingivalis) and its gingipain virulence factors have been identified as pathogenic effectors in Alzheimer's disease (AD). In a recent study we demonstrated the presence of gingipains in over 90% of postmortem AD brains, with gingipains localizing to the cytoplasm of neurons. However, infection of neurons by P. gingivalis has not been previously reported. Objective: To demonstrate intraneuronal P. gingivalis and gingipain expression in vitro after infecting neurons derived from human inducible pluripotent stem cells (iPSC) with P. gingivalis for 24, 48, and 72 h. Methods: Infection was characterized by transmission electron microscopy, confocal microscopy, and bacterial colony forming unit assays. Gingipain expression was monitored by immunofluorescence and RT-qPCR, and protease activity monitored with activity-based probes. Neurodegenerative endpoints were assessed by immunofluorescence, western blot, and ELISA. Results: Neurons survived the initial infection and showed time dependent, infection induced cell death. P. gingivalis was found free in the cytoplasm or in lysosomes. Infected neurons displayed an accumulation of autophagic vacuoles and multivesicular bodies. Tau protein was strongly degraded, and phosphorylation increased at T231. Over time, the density of presynaptic boutons was decreased. Conclusion: P. gingivalis can invade and persist in mature neurons. Infected neurons display signs of AD-like neuropathology including the accumulation of autophagic vacuoles and multivesicular bodies, cytoskeleton disruption, an increase in phospho-tau/tau ratio, and synapse loss. Infection of iPSC-derived mature neurons by P. gingivalis provides a novel model system to study the cellular mechanisms leading to AD and to investigate the potential of new therapeutic approaches.

Background: Porphyromonas gingivalis (P. gingivalis) and its gingipain virulence factors have been identified as pathogenic effectors in Alzheimer's disease (AD). In a recent study we demonstrated the presence of gingipains in over 90% of postmortem AD brains, with gingipains localizing to the cytoplasm of neurons. However, infection of neurons by P. gingivalis has not been previously reported. Objective: To demonstrate intraneuronal P. gingivalis and gingipain expression in vitro after infecting neurons derived from human inducible pluripotent stem cells (iPSC) with P. gingivalis for 24, 48, and 72 h. Methods: Infection was characterized by transmission electron microscopy, confocal microscopy, and bacterial colony forming unit assays. Gingipain expression was monitored by immunofluorescence and RT-qPCR, and protease activity monitored with activity-based probes. Neurodegenerative endpoints were assessed by immunofluorescence, western blot, and ELISA. Results: Neurons survived the initial infection and showed time dependent, infection induced cell death. P. gingivalis was found free in the cytoplasm or in lysosomes. Infected neurons displayed an accumulation of autophagic vacuoles and multivesicular bodies. Tau protein was strongly degraded, and phosphorylation increased at T231. Over time, the density of presynaptic boutons was decreased. Conclusion: P. gingivalis can invade and persist in mature neurons. Infected neurons display signs of AD-like neuropathology including the accumulation of autophagic vacuoles and multivesicular bodies, cytoskeleton disruption, an increase in phospho-tau/tau ratio, and synapse loss. Infection of iPSC-derived mature neurons by P. gingivalis provides a novel model system to study the cellular mechanisms leading to AD and to investigate the potential of new therapeutic approaches.

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties., Comment: 13 pages and 6 figures. Revised/edited for clarity and purpose. Several references added. Updated title based on suggestions and comments received. Version accepted for publication in Phys.Rev.B

We outline the duality between the extraordinary magnetoresistance (EMR), observed in semiconductor-metal hybrids, and non-symmetric gravity coupled to a diffusive $U(1)$ gauge field. The corresponding gravity theory may be interpreted as the generalized complex geometry of the semi-direct product of the symmetric metric and the antisymmetric Kalb-Ramond field: ($g_{\mu\nu}+\beta_{\mu\nu}$). We construct the four dimensional covariant field theory and compute the resulting equations of motion. The equations encode the most general form of EMR within a well defined variational principle, for specific lower dimensional embedded geometric scenarios. Our formalism also reveals the emergence of additional diffusive pseudo currents for a completely dynamic field theory of EMR. The proposed equations of motion now include terms that induce geometrical deformations in the device geometry in order to optimize the EMR. This bottom-up dual description between EMR and generalized geometry/gravity lends itself to a deeper insight into the EMR effect with the promise of potentially new physical phenomena and properties., Comment: 13 pages and 6 figures. Revised/edited for clarity and purpose. Several references added. Updated title based on suggestions and comments received. Version accepted for publication in Phys.Rev.B

We compute the full asymptotic symmetry group of black holes belonging to the same equivalence class of solutions within the Conformal Weyl Gravity formalism. We do this within an $AdS_2/CFT_1$ correspondence and by performing a Robinson-Wilczek two dimensional reduction, thus enabling the construction of an effective quantum theory of the remaining field content. The resulting energy momentum tensors generate asymptotic Virasoro algebras, to $s$-wave, with calculable central extensions. These centers in conjunction with their proper regularized lowest Virasoro eigen-modes yield the Bekenstein-Hawking black hole entropy via the statistical Cardy formula. We also analyze quantum holomorphic fluxes of the dual CFTs in the near horizon, giving rise to finite Hawking temperatures weighted by the central charges of the respective black hole spacetimes. We conclude with a discussion and outlook for future work., Comment: 18 pages, no figures. Accepted version contributed to mdpi's Universe collection on open questions in black hole physics

We compute the full asymptotic symmetry group of black holes belonging to the same equivalence class of solutions within the Conformal Weyl Gravity formalism. We do this within an $AdS_2/CFT_1$ correspondence and by performing a Robinson-Wilczek two dimensional reduction, thus enabling the construction of an effective quantum theory of the remaining field content. The resulting energy momentum tensors generate asymptotic Virasoro algebras, to $s$-wave, with calculable central extensions. These centers in conjunction with their proper regularized lowest Virasoro eigen-modes yield the Bekenstein-Hawking black hole entropy via the statistical Cardy formula. We also analyze quantum holomorphic fluxes of the dual CFTs in the near horizon, giving rise to finite Hawking temperatures weighted by the central charges of the respective black hole spacetimes. We conclude with a discussion and outlook for future work., Comment: 18 pages, no figures. Accepted version contributed to mdpi's Universe collection on open questions in black hole physics

We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of $AdS_2/CFT_1$ correspondence. We start by shifting the horizon of near horizon extremal Kerr (NHEK) geometry by a general finite mass. While this shift does not alter the geometry in that the resulting classical solution is still diffeomorphic to the NHEK solution, it does lead to a quantum theory different from that of NHEK. We obtain this quantum theory by means of a Robinson-Wilczek two-dimensional Kaluza-Klein reduction which enables us to introduce a finite regulator on the $AdS_2$ boundary and compute the full asymptotic symmetry group of the two-dimensional quantum conformal field theory on the respective $AdS_2$ boundary. The s-wave contribution of the energy-momentum-tensor of this conformal field theory, together with the asymptotic symmetries, generate a Virasoro algebra with a calculable center, which agrees with the standard Kerr/$CFT$ result, and a non-vanishing lowest Virasoro eigenmode. The central charge and lowest eigenmode produce the Bekenstein-Hawking entropy and Hawking temperature for NHNEK., Comment: Invited contribution to the proceedings of Quantum Fest 2015, which is dedicated to the memory of Sujeev Wickramasekara who passed away suddenly on December 28th 2015. Article based on arXiv:1206.2261

We study the thermodynamics of near horizon near extremal Kerr (NHNEK) geometry within the framework of $AdS_2/CFT_1$ correspondence. We start by shifting the horizon of near horizon extremal Kerr (NHEK) geometry by a general finite mass. While this shift does not alter the geometry in that the resulting classical solution is still diffeomorphic to the NHEK solution, it does lead to a quantum theory different from that of NHEK. We obtain this quantum theory by means of a Robinson-Wilczek two-dimensional Kaluza-Klein reduction which enables us to introduce a finite regulator on the $AdS_2$ boundary and compute the full asymptotic symmetry group of the two-dimensional quantum conformal field theory on the respective $AdS_2$ boundary. The s-wave contribution of the energy-momentum-tensor of this conformal field theory, together with the asymptotic symmetries, generate a Virasoro algebra with a calculable center, which agrees with the standard Kerr/$CFT$ result, and a non-vanishing lowest Virasoro eigenmode. The central charge and lowest eigenmode produce the Bekenstein-Hawking entropy and Hawking temperature for NHNEK., Comment: Invited contribution to the proceedings of Quantum Fest 2015, which is dedicated to the memory of Sujeev Wickramasekara who passed away suddenly on December 28th 2015. Article based on arXiv:1206.2261

We compute the asymptotic symmetry group of the four dimensional near-extremal Kerr-Sen black hole within an AdS2/CFT1 correspondence. We do this by performing a Robinson-Wilczek two dimensional reduction and construct a quantum theory of the remaining field content. The resulting energy momentum tensor generates an asymptotic Virasoro algebra, to s-wave, with a calculable central extension. This center in conjunction with the proper regularized lowest Virasoro eigen-mode yields the near-extremal Kerr-Sen entropy via the statistical Cardy formula. Finally we analyze quantum holomorphic fluxes of the dual CFT giving rise to a finite Hawking temperature weighted by the central charge of the near-extremal Kerr-Sen metric., Comment: 16 pages, references added, revised for clarity. To appear in JHEP

We compute the asymptotic symmetry group of the four dimensional near-extremal Kerr-Sen black hole within an AdS2/CFT1 correspondence. We do this by performing a Robinson-Wilczek two dimensional reduction and construct a quantum theory of the remaining field content. The resulting energy momentum tensor generates an asymptotic Virasoro algebra, to s-wave, with a calculable central extension. This center in conjunction with the proper regularized lowest Virasoro eigen-mode yields the near-extremal Kerr-Sen entropy via the statistical Cardy formula. Finally we analyze quantum holomorphic fluxes of the dual CFT giving rise to a finite Hawking temperature weighted by the central charge of the near-extremal Kerr-Sen metric., Comment: 16 pages, references added, revised for clarity. To appear in JHEP

We study the thermodynamics of the near horizon of near extremal Kerr geometry (near-NHEK) within an AdS2/CFT1 correspondence. We do this by shifting the horizon by a general finite mass, which does not alter the geometry and the resulting solution is still diffeomorphic to NHEK, however it allows for a Robertson Wilczek two dimensional Kaluza-Klein reduction and the introduction of a finite regulator on the AdS2 boundary. The resulting asymptotic symmetry group of the two dimensional Kaluza-Klein reduction leads to a non-vanishing quantum conformal field theory on the respective AdS2 boundary. The s-wave contribution of the energy-momentum-tensor of the CFT, together with the asymptotic symmetries, generate a Virasoro algebra with calculable center and non-vanishing lowest Virasoro eigen-mode. The central charge and lowest eigen-mode reproduce the near-NHEK Bekenstein-Hawking entropy via the statistical Cardy Formula and our derived central charge agrees with the standard Kerr/CFT Correspondence. We also compute the Hawking temperature of the shifted near-NHEK by analyzing quantum holomorphic fluxes of the Robinson and Wilczek two dimensional analogue fields., Comment: 24 pages. References added and shortened introduction. Typos corrected, edits and revisions performed in accord with comments and suggestions received

We study the thermodynamics of the near horizon of near extremal Kerr geometry (near-NHEK) within an AdS2/CFT1 correspondence. We do this by shifting the horizon by a general finite mass, which does not alter the geometry and the resulting solution is still diffeomorphic to NHEK, however it allows for a Robertson Wilczek two dimensional Kaluza-Klein reduction and the introduction of a finite regulator on the AdS2 boundary. The resulting asymptotic symmetry group of the two dimensional Kaluza-Klein reduction leads to a non-vanishing quantum conformal field theory on the respective AdS2 boundary. The s-wave contribution of the energy-momentum-tensor of the CFT, together with the asymptotic symmetries, generate a Virasoro algebra with calculable center and non-vanishing lowest Virasoro eigen-mode. The central charge and lowest eigen-mode reproduce the near-NHEK Bekenstein-Hawking entropy via the statistical Cardy Formula and our derived central charge agrees with the standard Kerr/CFT Correspondence. We also compute the Hawking temperature of the shifted near-NHEK by analyzing quantum holomorphic fluxes of the Robinson and Wilczek two dimensional analogue fields., Comment: 24 pages. References added and shortened introduction. Typos corrected, edits and revisions performed in accord with comments and suggestions received

This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields., Comment: 47 pages, reworded text relating to central charges, renumbered pages, updated title page and references

This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields., Comment: 47 pages, reworded text relating to central charges, renumbered pages, updated title page and references

We show that the near horizon regime of a Kerr-Newman-$AdS$ (KN$AdS$) black hole, given by its two dimensional analogue $a la$ Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), is asymptotically $AdS_2$ and dual to a one dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy-momentum-tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein-Hawking entropy via Cardy's Formula. Our derived central charge also agrees with the near extremal Kerr/CFT Correspondence (2009 Phys. Rev. D 80, 124008) in the appropriate limits. We also compute the Hawking temperature of the KN$AdS$ black hole by coupling its Robinson and Wilczek two dimensional analogue (RW2DA) to conformal matter., Comment: 15 pages. Major edits and revisions. Final version accepted for publication in IJMPA

We construct a 2-dimensional CFT, in the form of a Liouville theory, in the near horizon limit of 4- and 3-dimensional black holes. The near horizon CFT assumes 2-dimensional black hole solutions first introduced by Christensen and Fulling and expanded to a greater class of black holes via Robinson and Wilczek. The 2-dimensional black holes admit a Diff($S^1$) subalgebra, which upon quantization in the horizon limit becomes Virasoro with calculable central charge. This charge and lowest Virasoro eigen-mode reproduce the correct Bekenstein-Hawking entropy of the 4- and 3-dimensional black holes via the known Cardy formula. Furthermore, the 2-dimensional CFT's energy momentum tensor is anomalous. However, In the horizon limit the energy momentum tensor becomes holomorphic equaling the Hawking flux of the 4- and 3-dimensional black holes. This encoding of both entropy and temperature provides a uniformity in the calculation of black hole thermodynamic and statistical quantities for the non local effective action approach., Comment: 18 pages, references added, accepted in IOP's Classical and Quantum Gravity.

An important operation in generalized complex geometry is the Courant bracket which extends the Lie bracket that acts only on vectors to a pair given by a vector and a p-form. We explore the possibility of promoting the elements of the Courant bracket to physical fields by constructing a geometric action based on the Kirillov-Kostant symplectic form. For the $p=0$ forms, the action generalizes Polyakov's two-dimensional quantum gravity when viewed as the geometric action for the Virasoro algebra. We show that the geometric action arising from the centrally extended Courant bracket for the vector and zero form pair is similar to the geometric action obtained from the semi-direct product of the Virasoro algebra with a U(1) affine Kac-Moody algebra. For arbitrary $p$ restricted to a Dirac structure, we derived the geometric action and exhibit generalizations for almost complex structures built on the Kirillov-Kostant symplectic form. In the case of p+1 dimensional submanifolds, we also discuss a generalization of a Kahler structure on the orbits., Comment: 31 pages, 2 figures Corrected various mistakes, added content on Kahler geometry and gneralizations of complex structures for orbits of the Courant bracket