We study the quantum-mechanical corrections to two point particles accelerated by a strut in a 2+1 D flat background. Since the particles are accelerating, we use finite temperature techniques to compute the Green's function of a conformally coupled scalar applying transparent and Dirichlet boundary conditions at the location of the strut. We find that the induced energy-momentum tensor diverges at the position of the strut unless we impose transparent boundary conditions. Further, we use the regular form of the induced energy-momentum tensor to calculate the gravitational backreaction on the original space. The resulting metric is a constant $ϕ$ section of the 4-dimensional C-metric, and it describes two black holes corrected by weakly coupled CFT and accelerating in asymptotically flat spacetime. Interestingly enough, the same form of the metric was obtained before in 0803.2242 by cutting the AdS C-metric with angular dependent critical 2-brane. According to AdS/CFT+gravity conjecture, the latter should describe strongly coupled CFT black holes accelerating on the brane. The presence of the CFT at finite temperature gives us a unique opportunity to study the AdS/CFT+gravity conjecture at finite temperatures. We calculate various thermodynamic parameters to shed light on the nature of the strongly coupled CFT. This is the first use of the duality in a system containing accelerating particles on the brane.
Vacuum structure and global cosmic strings are analyzed in the effective theory of self-interacting O(2) scalar fields on (3+1)-manifolds with conical singularities. In the context of one-loop effective action computed by heat-kernel methods with $ζ$-function regularization, we find an inhomogeneous vacuum of minimum energy and suggest some reason why low-energy global strings are likely to be generated at the conical singularities.
One-loop effects for quantum fields living on manifolds containing conical singularities are investigated in the context of cosmic string background and of finite-temperature theory in the Rindler wedge or outside the horizon of a Schwarzschild black-hole.
We introduce a new set of chemical variables for the accelerating black hole. We show how these expressions suggest that conical defects emerging from a black hole can be considered as true hair -- a new charge that the black hole can carry -- and discuss the impact of conical deficits on black hole thermodynamics from this `chemical' perspective. We conclude by proving a new {\it Reverse Isoperimetric Inequality} for black holes with conical defects.
We argue that, when working with the appropriate set of thermodynamical variables, the Bekenstein-Hawking law still holds for asymptotically flat black objects with conical singularities. The mass-energy which enters the first law of thermodynamics does not, however, coincide with the ADM mass; it differs from the latter by the energy associated with the conical singularity, as seen by an asymptotic, static observer. These statements are supported by a number of examples: the Bach-Weyl (double-Schwarzschild) solution, its dihole generalisation in Einstein-Maxwell theory and the five dimensiona…
Free and self-interacting scalar fields in the presence of conical singularities are analized in some detail. The role of such a kind of singularities on free and vacuum energy and also on the one-loop effective action is pointed out using $ζ$-function regularization and heat-kernel techniques.
We present mechanisms for generating conical singularities both in three and four-dimensions in the systems with copies of scalar or chiral multiplets coupled to $N=2$ or $N=1$ supergravity. Our mechanisms are useful for supersymmetry breaking, maintaining the zero cosmological constants in three and four-dimensions. A strong coupling duality connecting these two dimensionalities is also studied.
We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.
We construct 7-dimensional compact Einstein spaces with conical singularities that preserve 1/8 of the supersymmetries of M-theory. Mathematically they have weak G_2-holonomy. We show that for every non-compact G_2-holonomy manifold which is asymptotic to a cone on a 6-manifold Y, there is a corresponding weak G_2-manifold with two conical singularities which, close to the singularities, looks like a cone on Y. Our construction provides explicit metrics on these weak G_2-manifolds. We completely determine the cohomology of these manifolds in terms of the cohomology of Y.
We consider the entropy of higher spin black holes in 2+1 dimensions using the conical singularity approach. By introducing a conical singularity along a non contractible cycle and carefully evaluating its contribution to the Chern Simons action, we derive a simple expression for the entropy of a general stationary higher spin black hole. The resulting formula is shown to satisfy the first law of thermodynamics, and yields agreement with previous results based on integrating the first law.
In this presentation, I review recent work with Mike Appels and David Kubiznak on thermodynamics of accelerating black holes. I start by reviewing the geometry of accelerating black holes, focussing on the conical deficit responsible for the 'force' causing the black hole to accelerate. Then I discuss black hole thermodynamics with conical deficits, showing how to include the tension of the deficit as a thermodynamic variable, and introducing a canonically conjugate {\it thermodynamic length}. Finally, I describe the thermodynamics of the slowly accelerating black hole in anti-de Sitter spacet…
Using the ``complexity equals action''(CA) conjecture, for an ordinary charged system, it has been shown that the late-time complexity growth rate is given by a difference between the value of $Φ_{H}Q+Ω_H J$ on the inner and outer horizons. In this paper, we investigate the complexity of the boundary quantum system with conical deficits. From the perspective of holography, we consider a charged accelerating black holes which contain conical deficits on the north and south poles in the bulk gravitational theory and evaluate the complexity growth rate using the CA conjecture. As a result, the la…
We study the regularization of the codimension-2 singularities in six-dimensional Einstein-Maxwell axisymmetric models with warping. These singularities are replaced by codimension-1 branes of a ring form, situated around the axis of symmetry. We assume that there is a brane scalar field with Goldstone dynamics, which is known to generate a brane energy momentum tensor of a particular structure necessary for the above regularization to be successful. We study these compactifications in both a non-supersymmetric and a supersymmetric setting. We see that in the non-supersymmetric case, there is …
Geometrical form of the one-loop divergences induced by conical singularities of background manifolds is studied. To this aim the heat kernel asymptotic expansion on spaces having the structure $C_α\times Σ$ near singular surface $Σ$ is analysed. Surface corrections to standard second and third heat coefficients are obtained explicitly in terms of angle $α$ of a cone $C_α$ and components of the Riemann tensor. These results are compared to ones to be already known for some particular cases. Physical aspects of the surface divergences are shortly discussed.
M-theory is known to possess supersymmetric solutions where the geometry is $\mathrm{AdS}_3\times S^3\times S^3$ warped over a Riemann surface $Σ_{2}$. The simplest examples in this class can be engineered by placing M2 and M5 branes as defects inside of a stack of background M5 branes. In this paper we show that a generalization of this construction yields more general solutions in the aforementioned class. The background branes are now M5's carrying M2 brane charge, while the defect branes are now placed at the origin of a flat hyperplane with a conical defect. The equations of motion imply …
We discuss the regularization of codimension-2 singularities in warped six-dimensional Einstein-Maxwell axisymmetric models by replacing them by codimension-1 branes of a ring form, situated around the axis of symmetry. Further we consider the case of one capped regularized conical brane of codimension one and study the cosmological evolution which is induced on it as it moves in between the known {\it static} bulk and cap solutions. We present the resulting brane Friedmann equation which gives a dominant five-dimensional $ρ^2$ energy density term at high energies and a term linear to the ener…
We show that the real-valued function $S_α$ on the moduli space $\mathcal{M}_{0,n}$ of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with $n\geq 3$ conical singularities of arbitrary orders $α=\{α_1,...,α_n\}$, generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kaehler metrics on $\mathcal{M}_{0,n}$ parameterized by the set of orders $α$, explictly relate accessory parameters to these metrics, and prove that the functions $S_α$ are their Kae…
For a general maximally symmetric (spherically, plane or hyperbola symmetric) holographic screen, we rewrite the equations of motion of general Lovelock gravity into the form of some generalized first law of thermodynamics, under certain ansatz. With this observation together with other two independent ways, exactly the same temperature and entropy on the screen are obtained. So it is argued that the thermodynamic interpretation of gravity is physically meaningful not only on the horizon, but also on a general maximally symmetric screen. Moreover, the formula of entropy is further checked in t…
Boundary conditions and the corresponding states of a quantum field theory depend on how the horizons are taken into account. There is ambiguity as to which method is appropriate because different ways of incorporating the horizons lead to different results. We propose that a natural way of including the horizons is to first consider the Kruskal extension and then define the quantum field theory on the Euclidean section. Boundary conditions emerge naturally as consistency conditions of the Kruskal extension. We carry out the proposal for the explicit case of the Schwarzschild-de Sitter manifol…
The spherical domains $S^d_β$ with conical singularities are a convenient arena for studying the properties of tensor Laplacians on arbitrary manifolds with such a kind of singular points. In this paper the vector Laplacian on $S^d_β$ is considered and its spectrum is calculated exactly for any dimension $d$. This enables one to find the Schwinger-DeWitt coefficients of this operator by using the residues of the $ζ$-function. In particular, the second coefficient, defining the conformal anomaly, is explicitly calculated on $S^d_β$ and its generalization to arbitrary manifolds is found. As an a…
In a class of Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, we derive both vacuum and interior Schwarzschild solutions under the condition that the derivatives of a scalar field $ϕ$ with respect to the radius $r$ vanish. If the parameter $α_{\rm H}$ characterizing the deviation from Horndeski theories approaches a non-zero constant at the center of a spherically symmetric body, we find that the conical singularity arises at $r=0$ with the Ricci scalar given by $R=-2α_{\rm H}/r^2$. This originates from violation of the geometrical structure of four-dimensional curvature quantities. The coni…
Using a solution-generating method, we derive an exact solution of the Einstein's field equations in five dimensions describing multi-black hole configurations. More specifically, this solution describes systems of non-extremal static black holes with Kaluza-Klein asymptotics. As expected, we find that, in general, there are conical singularities in-between the Kaluza-Klein black holes that cannot be completely eliminated. Notwithstanding the presence of these conical singularities, such solutions still exhibit interesting thermodynamical properties. By choosing an appropriate set of thermodyn…
This is the first in a series of five papers math.DG/0211295, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated singularities at 0. Readers are advised to begin with the final paper math.DG/0303272, which surveys the series, gives examples, and applies the results to prove some conjectures. This first paper lays the foundations for the series, giving definitions and proving auxiliary results in symp…
In Gleyzes-Langlois-Piazza-Vernizzi (GLPV) theories, it is known that the conical singularity arises at the center of a spherically symmetric body ($r=0$) in the case where the parameter $α_{{\rm H}4}$ characterizing the deviation from the Horndeski Lagrangian $L_4$ approaches a non-zero constant as $r \to 0$. We derive spherically symmetric solutions around the center in full GLPV theories and show that the GLPV Lagrangian $L_5$ does not modify the divergent property of the Ricci scalar $R$ induced by the non-zero $α_{{\rm H}4}$. Provided that $α_{{\rm H}4}=0$, curvature scalar quantities can…
This is the last in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0302356 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated singularities at 0. Readers are advised to begin with this paper. We survey the major results of the previous four papers, giving brief explanations of the proofs. We apply the results to describe the boundary of a moduli space of compact, nonsingular SL m-folds N in M. We prove the…
We study solutions in the Plebański--Demiański family which describe an accelerating, rotating and dyonically charged black hole in $AdS_4$. These are solutions of $D=4$ Einstein-Maxwell theory with a negative cosmological constant and hence minimal $D=4$ gauged supergravity. It is well known that when the acceleration is non-vanishing the $D=4$ black hole metrics have conical singularities. By uplifting the solutions to $D=11$ supergravity using a regular Sasaki-Einstein $7$-manifold, $SE_7$, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, …
For supergavrity solutions which are the product of an anti-de Sitter space with an Einstein space X, we study the relation between the amount of supersymmetry preserved and the geometry of X. Depending on the dimension and the amount of supersymmetry, the following geometries for X are possible, in addition to the maximally supersymmetric spherical geometry: Einstein-Sasaki in dimension 2k+1, 3-Sasaki in dimension 4k+3, 7-dimensional manifolds of weak G_2 holonomy and 6-dimensional nearly Kaehler manifolds. Many new examples of such manifolds are presented which are not homogeneous and have e…
This is the second in a series of five papers math.DG/0211294, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated singularities at 0. Readers are advised to begin with the final paper math.DG/0303272 which surveys the series, gives examples, and proves some conjectures. In this paper we study the deformation theory of compact SL m-folds X in M with conical singularities. We define the moduli space M_…
The existence of two metrics in massive gravity theories in principle allows solutions where there are singularities in new scalar invariants jointly constructed from them. These configurations occur when the two metrics differ substantially from each other, as in black hole and cosmological solutions. The simplest class of such singularities are determinant singularities. We investigate whether the dynamics of bimetric massive gravity -- where the second metric is allowed to evolve jointly with the spacetime metric -- can avoid these singularities. We investigate whether the dynamics of bimet…
We investigate the functional determinant of the laplacian on piece-wise flat two-dimensional surfaces, with conical singularities in the interior and/or corners on the boundary. Our results extend earlier investigations of the determinants on smooth surfaces with smooth boundaries. The differences to the smooth case are: a) different ``interaction energies'' between pairs of conical singularities than one would expect from a naive extrapolation of the results for a smooth surface; and b) ``self-energies'' of the singularities.
When M-theory is compactified on G_2-holonomy manifolds with conical singularities, charged chiral fermions are present and the low-energy four-dimensional theory is potentially anomalous. We reconsider the issue of anomaly cancellation, first studied by Witten. We propose a mechanism that provides local cancellation of all gauge and mixed gauge-gravitational anomalies, i.e. separately for each conical singularity. It is similar in spirit to the one used to cancel the normal bundle anomaly in the presence of five-branes. It involves smoothly cutting off all fields close to the conical singular…
Placing D3-branes at conical Calabi-Yau threefold singularities produces many AdS$_5$/CFT$_4$ duals. Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics. On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity. In this paper, we put together these ideas to produce new AdS$_5$/CFT$_4$ duals, with special emphasis on non-toric singularities.
A consistent approach to the description of integral coordinate invariant functionals of the metric on manifolds ${\cal M}_α$ with conical defects (or singularities) of the topology $C_α\timesΣ$ is developed. According to the proposed prescription ${\cal M}_α$ are considered as limits of the converging sequences of smooth spaces. This enables one to give a strict mathematical meaning to a number of invariant integral quantities on ${\cal M}_α$ and make use of them in applications. In particular, an explicit representation for the Euler numbers and Hirtzebruch signature in the presence of conic…
We prove that any totally geodesic hypersurface $N^5$ of a 6-dimensional nearly Kähler manifold $M^6$ is a Sasaki-Einstein manifold, and so it has a hypo structure in the sense of \cite{ConS}. We show that any Sasaki-Einstein 5-manifold defines a nearly Kähler structure on the sin-cone $N^5\times\mathbb R$, and a compact nearly Kähler structure with conical singularities on $N^5\times [0,π]$ when $N^5$ is compact thus providing a link between Calabi-Yau structure on the cone $N^5\times [0,π]$ and the nearly Kähler structure on the sin-cone $N^5\times [0,π]$. We define the notion of {\it nearly…
This is the fourth in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302355, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated singularities at 0. Readers are advised to begin with the final paper math.DG/0303272 which surveys the series, gives examples, and applies the results to prove some conjectures. The first paper math.DG/0211294 studied the regularity of X near its singular points, and the second m…
This is the third in a series of five papers math.DG/0211294, math.DG/0211295, math.DG/0302356, math.DG/0303272 studying compact special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally modelled on special Lagrangian cones C_1,...,C_n in C^m with isolated singularities at 0. Readers are advised to begin with the final paper math.DG/0303272 which surveys the series, gives examples, and applies the results to prove some conjectures. The first two papers math.DG/0211294, math.DG/0211295 studied the regularity of X near its singular poi…
The Taubes equation for Abelian Higgs vortices is generalised to five distinct U(1) vortex equations. These include the Popov and Jackiw--Pi vortex equations, and two new equations. The Baptista metric, a conformal rescaling of the background metric by the squared Higgs field, gives insight into these vortices, and shows that vortices can be interpreted as conical singularities superposed on the background geometry. When the background has a constant curvature adapted to the vortex type, then the vortex equation is integrable by a reduction to Liouville's equation, and the Baptista metric has …
