Strings near black holes are Carrollian

Bagchi, Arjun; Banerjee, Aritra; Hartong, Jelle; Have, Emil; Kolekar, Kedar S.; Mandlik, Mangesh

doi:10.1103/physrevd.110.086009

Phys. Rev. D

2024

DOI: 10.1103/physrevd.110.086009

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Strings near black holes are Carrollian

Arjun Bagchi,

Aritra Banerjee,

Jelle Hartong

et al.

Abstract: We demonstrate that strings near the horizon of a Schwarzschild black hole, when viewed by a stationary observer at infinity, probe a string Carroll geometry, where the effective light speed is given by the distance from the horizon. We expand the Polyakov action in powers of this light speed to find a theory of Carrollian strings. We show that the string shrinks to a point to leading order near the horizon, which follows a null geodesic in a two-dimensional Rindler space. At the next-to-leading order the stri… Show more

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2024

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Cited by 2 publications

References 61 publications

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3d Carrollian Chern-Simons theory & 2d Yang-Mills

Bagchi,

Lipstein,

Mandlik

et al. 2024

J. High Energ. Phys.

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With the goal of building a concrete co-dimension one holographically dual field theory for four dimensional asymptotically flat spacetimes (4d AFS) as a limit of AdS4/CFT3, we begin an investigation of 3d Chern-Simons matter (CSM) theories in the Carroll regime. We perform a Carroll (speed of light c → 0) expansion of the relativistic Chern-Simons action coupled to a massless scalar and obtain Carrollian CSM theories, which we show are invariant under the infinite dimensional 3d conformal Carroll or 4d Bondi-van der Burg-Metzner-Sachs (BMS4) symmetries, thus making them putative duals for 4d AFS. Concentrating on the leading-order electric Carroll CSM theory, we perform a null reduction of the 3d theory. Null reduction is a procedure to obtain non-relativistic theories from a higher dimensional relativistic theory. Curiously, null reduction of a Carrollian theory yields a relativistic lower-dimensional theory. We work with SU(N) × SU(M) CS theory coupled to bi-fundamental matter and show that when N = M, we obtain (rather surprisingly) a 2d Euclidean Yang-Mills theory after null reduction. We also comment on the reduction when N ≠ M and possible connections of the null-reduced Carroll theory to a candidate 2d Celestial CFT.

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3d Carrollian Chern-Simons theory & 2d Yang-Mills

Bagchi,

Lipstein,

Mandlik

et al. 2024

J. High Energ. Phys.

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Strings near black holes are Carrollian. Part II

Bagchi,

Banerjee,

Hartong

et al. 2024

J. High Energ. Phys.

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We study classical closed bosonic strings probing the near-horizon region of a non-extremal black hole and show that this corresponds to understanding string theory in the Carroll regime. This is done by first performing a Carroll expansion and then a near-horizon expansion of a closed relativistic string, subsequently showing that they agree. Concretely, we expand the phase space action in powers of c2, where c is the speed of light, assuming that the target space admits a string Carroll expansion (where two directions are singled out) and show that there exist two different Carroll strings: a magnetic and an electric string. The magnetic string has a Lorentzian worldsheet, whereas the worldsheet of the electric string is Carrollian. The geometry near the horizon of a four-dimensional (4D) Schwarzschild black hole takes the form of a string Carroll expansion (a 2D Rindler space fibred over a 2-sphere). We show that the solution space of relativistic strings near the horizon bifurcates and the two sectors precisely match with the magnetic/electric Carroll strings with an appropriate target space. Magnetic Carroll strings near a black hole shrink to a point on the two-sphere and either follow null geodesics or turn into folded strings on the 2D Rindler spacetime. Electric Carroll strings wrap the two-sphere and follow a massive geodesic in the Rindler space. Finally, we show that 4D non-extremal Kerr and Reissner-Nordström black holes also admit string Carroll expansions near their outer horizons, indicating that our formulation extends to generic non-extremal black holes.

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Strings near black holes are Carrollian

Cited by 2 publications

References 61 publications

3d Carrollian Chern-Simons theory & 2d Yang-Mills

3d Carrollian Chern-Simons theory & 2d Yang-Mills

Strings near black holes are Carrollian. Part II

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