Fuzzballs with internal excitations

Abstract: We construct general 2-charge D1-D5 horizon-free non-singular solutions of IIB supergravity on T^4 and K3 describing fuzzballs with excitations in the internal manifold; these excitations are characterized by arbitrary curves. The solutions are obtained via dualities from F1-P solutions of heterotic and type IIB on T^4 for the K3 and T^4 cases, respectively. We compute the holographic data encoded in these solutions, and show that the internal excitations are captured by vevs of chiral primaries associated with the middle cohomology of T^4 or K3. We argue that each geometry is dual to a specific superposition of R ground states determined in terms of the Fourier coefficients of the curves defining the supergravity solution. We compute vevs of chiral primaries associated with the middle cohomology and show that they indeed acquire vevs in the superpositions corresponding to fuzzballs with internal excitations, in accordance with the holographic results. We also address the question of whether the fuzzball program can be implemented consistently within supergravity.

• The paper constructs non-singular D1-D5 fuzzball geometries by mapping F1-P solitons through dualities to model black hole microstates.
• It demonstrates that internal excitations represented by arbitrary curves yield specific holographic vevs for chiral primary operators.
• The research highlights the efficacy of the fuzzball paradigm in supergravity while indicating the need for quantum corrections to capture full microstate details.

Exploration of Fuzzballs with Internal Excitations in Supergravity

The paper "Fuzzballs with internal excitations" by Kanitscheider, Skenderis, and Taylor explores the intricate landscape of fuzzy structures within supergravity frameworks, specifically focusing on the holographic representation of black hole microstates. The authors explore two-charge D1-D5 configurations, devoid of horizons, in IIB supergravity compactified on $T^4$ and K3 surfaces. The principal aim is to understand the role of excitations within the internal manifold, characterized by arbitrary curves, and their dual interpretation via holography.

Construction of Horizon-Free Solutions

The authors construct non-singular solutions by utilizing dualities from heterotic F1-P systems and type IIB on $T^4$ to articulate solutions on K3. These dualities are imperative in translating excitations, initially represented by curves in the F1-P description, into the D1-D5 framework. The transition involves T-duality, S-duality, and type II string-string duality, enabling the mapping of solitonic string solutions to their geometrical counterparts in the D1-D5 system.

Holographic Encoding and Chiral Primaries

An essential aspect of their study is the computation of holographic data encapsulated by these fuzzball solutions. The internal excitations correspond to the vacuum expectation values (vevs) of chiral primaries linked to the middle cohomology of $T^4$ or K3. They demonstrate that each geometry corresponds to specific superpositions of R-ground states, ascertainable through Fourier coefficients of defining curves. Furthermore, the matching of geometrical transformations with their dual field theory states relies on the precise extraction of these holographic vevs.

Implications for the Fuzzball Program

The research addresses a fundamental query: whether the fuzzball paradigm can be consistently enacted within supergravity. They assert that while these constructions provide a comprehensive view of the gravity duals to black hole microstates, many intricate details necessitate considerations beyond classical supergravity. For example, certain microstates, especially those with small R-charges, may not be distinguishable within this classical framework, requiring insights from quantum corrections or string theory effects.

Concluding Remarks and Future Directions

The paper makes significant strides in advancing the fuzzball proposal, especially in elucidating how black hole properties potentially emerge from these horizon-free geometries. While the work primarily focuses on two-charge systems, the methodologies and insights presented are instrumental for further exploration of more complex black hole scenarios, including those with additional charges or in different dimensional settings. Future studies will likely extend these techniques to deeper understandings of black hole entropy, holographic duality, and perhaps elucidating the enigmatic information paradox within quantum gravity more precisely.

Overall, the paper stands as a pivotal contribution to the ongoing discourse on the microscopic structure of black holes and offers a robust framework for future investigations within supergravity and holographic duality.