arXiv subjects

G. Papadopoulos

Publications and source records attributed to G. Papadopoulos.

At least 55 records · Page 3Linked to original sources

arXiv2015

Estimation of connectivity measures in gappy time series

A new method is proposed to compute connectivity measures on multivariate time series with gaps. Rather than removing or filling the gaps, the rows of the joint data matrix containing empty entries are removed and the calculations are done on the remainder matrix. The method, called measure adapted gap removal (MAGR), can be applied to any connectivity measure that uses a joint data matrix, such as cross correlation, cross mutual information and transfer entropy. MAGR is favorably compared using these three measures to a number of known gap-filling techniques, as well as the gap closure. The superiority of MAGR is illustrated on time series from synthetic systems and financial time series.

stat.ME↗

arXiv2015

Supersymmetry of AdS and flat IIB backgrounds

We present a systematic description of all warped $AdS_n\times_w M^{10-n}$ and ${\mathbb{R}}^{n-1,1}\times_w M^{10-n}$ IIB backgrounds and identify the a priori number of supersymmetries $N$ preserved by these solutions. In particular, we find that the $AdS_n$ backgrounds preserve $N=2^{[{n\over2}]} k$ for $n\leq 4$ and $N=2^{[{n\over2}]+1} k$ for $4<n\leq 6$ supersymmetries and for $k\in {\mathbb{N}}_{+}$ suitably restricted. In addition under some assumptions required for the applicability of the maximum principle, we demonstrate that the Killing spinors of $AdS_n$ backgrounds can be identified with the zero modes of Dirac-like operators on $M^{10-n}$ establishing a new class of Lichnerowicz type theorems. Furthermore, we adapt some of these results to ${\mathbb{R}}^{n-1,1}\times_w M^{10-n}$ backgrounds with fluxes by taking the AdS radius to infinity. We find that these backgrounds preserve $N=2^{[{n\over2}]} k$ for $2<n\leq 4$ and $N=2^{[{n+1\over2}]} k$ for $4<n\leq 7$ supersymmetries. We also demonstrate that the Killing spinors of $AdS_n\times_w M^{10-n}$ do not factorize into Killing spinors on $AdS_n$ and Killing spinors on $M^{10-n}$.

hep-th↗

arXiv2015

Supersymmetry of IIA warped flux AdS and flat backgrounds

We identify the fractions of supersymmetry preserved by the most general warped flux AdS and flat backgrounds in both massive and standard IIA supergravities. We find that $AdS_n\times_w M^{10-n}$ preserve $2^{[{n\over2}]} k$ for $n\leq 4$ and $2^{[{n\over2}]+1} k$ for $4 0}$. In addition we show that, for suitably restricted fields and $M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the zero modes of Dirac like operators on $M^{10-n}$. This generalizes the Lichnerowicz theorem for connections whose holonomy is included in a general linear group. We also adapt our results to $\bR^{1,n-1}\times_w M^{10-n}$ backgrounds which underpin flux compactifications to $\bR^{1,n-1}$ and show that these preserve $2^{[{n\over2}]} k$ for $2<n\leq 4$, $2^{[{n+1\over2}]} k$ for $4<n\leq 8$, and $2^{[{n\over2}]} k$ for $n=9, 10$ supersymmetries.

hep-th↗

arXiv2014

Dynamical symmetry enhancement near massive IIA horizons

We prove that Killing horizons in massive IIA supergravity preserve an even number of supersymmetries, and that their symmetry algebra contains an $\mathfrak{sl}(2, R)$ subalgebra, confirming the conjecture of [5]. We also prove a new class of Lichnerowicz type theorems for connections of the spin bundle whose holonomy is contained in a general linear group.

hep-th↗

arXiv2014

Seeking the balance: Patching double and exceptional field theories

We investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength $H$ is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.

hep-th↗

arXiv2014

Dynamical symmetry enhancement near IIA horizons

We show that smooth type IIA Killing horizons with compact spatial sections preserve an even number of supersymmetries, and that the symmetry algebra of horizons with non-trivial fluxes includes an sl(2,R) subalgebra. This confirms the conjecture of [1] for type IIA horizons. As an intermediate step in the proof, we also demonstrate new Lichnerowicz type theorems for spin bundle connections whose holonomy is contained in a general linear group.

hep-th↗

arXiv2014

Supersymmetry of AdS and flat backgrounds in M-theory

We give a systematic description of all warped $AdS_n$ and ${\mathbb{R}}^{n-1,1}$ backgrounds of M-theory and identify the a priori number of supersymmetries that these backgrounds preserve. In particular, we show that $AdS_n$ backgrounds preserve $N= 2^{[{n\over2}]} k$ for $n\leq4$ and $N= 2^{[{n\over2}]+1} k$ for $4<n\leq 7$ supersymmetries while ${\mathbb{R}}^{n-1,1}$ backgrounds preserve $N= 2^{[{n\over2}]} k$ for $n\leq4$ and $N= 2^{[{n+1\over2}]} k$ for $4<n\leq7$, supersymmetries. Furthermore for $AdS_n$ backgrounds that satisfy the requirements for the maximum principle to hold, we show that the Killing spinors can be identified with the zero modes of Dirac-like operators on $M^{11-n}$ coupled to fluxes thus establishing a new class of Lichnerowicz type theorems. We also demonstrate that the Killing spinors of generic warped $AdS_n$ backgrounds do not factorize into products of Killing spinors on $AdS_n$ and Killing spinors on the transverse space.

hep-th↗

arXiv2014

Spinorial geometry, horizons and superconformal symmetry in six dimensions

The spinorial geometry method of solving Killing spinor equations is reviewed as it applies to 6-dimensional (1,0) supergravity. In particular, it is explained how the method is used to identify both the fractions of supersymmetry preserved by and the geometry of all supersymmetric backgrounds. Then two applications are described to systems that exhibit superconformal symmetry. The first is the proof that some 6-dimensional black hole horizons are locally isometric to $AdS_3\times Σ^3$, where $Σ^3$ is diffeomeorphic to $S^3$. The second one is a description of all supersymmetric solutions of 6-dimensional (1,0) superconformal theories and in particular of their brane solitons.

hep-th↗

arXiv2013

Brane solitons of (1,0) superconformal theories in six dimensions with hypermultiplets

We solve the Killing spinor equations of 6-dimensional (1,0) superconformal theories which include hyper-multiplets in all cases. We show that the solutions preserve 1,2,3,4 and 8 supersymmetries. We find models with self-dual string solitons which are smooth and supported by instantons with an arbitrary gauge group, and 3-brane solitons as expected from the M-brane intersection rules.

hep-th↗

arXiv2013

Index theory and dynamical symmetry enhancement near IIB horizons

We show that the number of supersymmetries of IIB black hole horizons is N=2 N_- + 2 index(D_λ), where index(D_λ) is the index of the Dirac operator twisted with the line bundle λ^{1/2} of IIB scalars, and N_- is the dimension of the kernel of a horizon Dirac operator which depends on IIB fluxes. Therefore, all IIB horizons preserve an even number of supersymmetries. In addition if the horizons have non-trivial fluxes and N_- is nonzero, then index(D_λ) is non-negative, and the horizons admit an sl(2,R) symmetry subalgebra. This provides evidence that all such horizons have an AdS/CFT dual. Furthermore if the orbits of sl(2,R) are two-dimensional, the IIB horizons are warped products AdS_2 X S.

hep-th↗

arXiv2013

Index theory and dynamical symmetry enhancement of M-horizons

We show that near-horizon geometries of 11-dimensional supergravity preserve an even number of supersymmetries. The proof follows from Lichnerowicz type theorems for two horizon Dirac operators, the field equations and Bianchi identities, and the vanishing of the index of a Dirac operator on the 9-dimensional horizon sections. As a consequence of this, we also prove that all M-horizons with non-vanishing fluxes admit a sl(2,R) subalgebra of symmetries.

hep-th↗

arXiv2013

IIB horizons

We solve the Killing spinor equations for all near-horizon IIB geometries which preserve at least one supersymmetry. We show that generic horizon sections are 8-dimensional almost Hermitian spin${}_c$ manifolds. Special cases include horizon sections with a $Spin(7)$ structure and those for which the Killing spinor is pure. We also explain how the common sector horizons and the horizons with only 5-form flux are included in our general analysis. We investigate several special cases mainly focusing on the horizons with constant scalars admitting a pure Killing spinor and find that some of these exhibit a generalization of the 2-SCYT condition that arises in the horizons with 5-form fluxes only. We use this to construct new examples of near-horizon geometries with both 3-form and 5-form fluxes.

hep-th↗

arXiv2012

M-Horizons

We solve the Killing spinor equations and determine the near horizon geometries of M-theory that preserve at least one supersymmetry. The M-horizon spatial sections are 9-dimensional manifolds with a Spin(7) structure restricted by geometric constraints which we give explicitly. We also provide an alternative characterization of the solutions of the Killing spinor equation, utilizing the compactness of the horizon section and the field equations, by proving a Lichnerowicz type of theorem which implies that the zero modes of a Dirac operator coupled to 4-form fluxes are Killing spinors. We use this, and the maximum principle, to solve the field equations of the theory for some special cases and present some examples.

hep-th↗

arXiv2012

New potentials for conformal mechanics

We find under some mild assumptions that the most general potential of 1-dimensional conformal systems with time independent couplings is expressed as $V=V_0+V_1$, where $V_0$ is a homogeneous function with respect to a homothetic motion in configuration space and $V_1$ is determined from an equation with source a homothetic potential. Such systems admit at most an $SL(2,\bR)$ conformal symmetry which, depending on the couplings, is embedded in Diff(R)$ in three different ways. In one case, $SL(2,\bR)$ is also embedded in Diff(S^1). Examples of such models include those with potential $V=αx^2+βx^{-2}$ for arbitrary couplings $α$ and $β$, the Calogero models with harmonic oscillator couplings and non-linear models with suitable metrics and potentials. In addition, we give the conditions on the couplings for a class of gauge theories to admit a $SL(2,\bR)$ conformal symmetry. We present examples of such systems with general gauge groups and global symmetries that include the isometries of $AdS_2 x S^3$ and $AdS_2 x S^3 x S^3$ which arise as backgrounds in $AdS_2/CFT_1$.

hep-th↗

arXiv2012

IIB black hole horizons with five-form flux and KT geometry

We investigate the near horizon geometry of IIB supergravity black holes with non-vanishing 5-form flux preserving at least two supersymmetries. We demonstrate that there are three classes of solutions distinguished by the choice of Killing spinors. We find that the spatial horizon sections of the class of solutions with an SU(4) invariant pure Killing spinor are hermitian manifolds and admit a hidden Kahler with torsion (KT) geometry compatible with the SU(4) structure. Moreover the Bianchi identity of the 5-form, which also implies the field equations, can be expressed in terms of the torsion H as d(ω\wedge H)=\partial\bar\partial ω^2=0, where omega is a Hermitian form. We give several examples of near horizon geometries which include group manifolds, group fibrations over KT manifolds and uplifted geometries of lower dimensional black holes. Furthermore, we show that the class of solutions associated with a Spin(7) invariant spinor is locally a product R^{1,1} x S, where S is a holonomy Spin(7) manifold.

hep-th↗

arXiv2011

Killing-Yano equations with torsion, worldline actions and G-structures

We determine the geometry of the target spaces of supersymmetric non-relativistic particles with torsion and magnetic couplings, and with symmetries generated by the fundamental forms of G-structures for $G= U(n), SU(n), Sp(n), Sp(n)\cdot Sp(1), G_2$ and $Spin(7)$. We find that the Killing-Yano equation, which arises as a condition for the invariance of the worldline action, does not always determine the torsion coupling uniquely in terms of the metric and fundamental forms. We show that there are several connections with skew-symmetric torsion for $G=U(n), SU(n)$ and $G_2$ that solve the invariance conditions. We describe all these compatible connections for each of the $G$-structures and explain the geometric nature of the couplings.

hep-th↗

arXiv2011

AdS backgrounds from black hole horizons

We utilize the classification of IIB horizons with 5-form flux to present a unified description for the geometry of AdS_n, n=3,5,7 solutions. In particular, we show that all such backgrounds can be constructed from 8-dimensional 2-strong Calabi-Yau geometries with torsion which admit some additional isometries. We explore the geometry of AdS_3 and AdS_5 solutions but we do not find AdS_7 solutions.

hep-th↗

arXiv2011

IIB black hole horizons with five-form flux and extended supersymmetry

We classify under some assumptions the IIB black hole horizons with 5-form flux preserving more than 2 supersymmetries. We find that the spatial horizon sections with non-vanishing flux preserving 4 supersymmetries are locally isometric either to S^1 * S^3 * T^4 or to S^1 * S^3 * K_3 and the associated near horizon geometries are locally isometric to AdS_3 * S^3 * T^4 and AdS_3 * S^3 * K_3$, respectively. The near horizon geometries preserving more than 4 supersymmetries are locally isometric to R^{1,1} * T^8.

hep-th↗