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Fully Funded EPSRC and STFC PhD Scholarship: Holography, Boundary Conformal Field Theory and the Black Hole Information Paradox

Department of Physics

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Prof P Kumar No more applications being accepted Funded PhD Project (Students Worldwide)

About the Project

This scholarship is funded by the Engineering and Physical Sciences Research Council (EPSRC) and Science and Technology Facilities Council (STFC).

Start date: October 2021


Project description:

This theoretical project will develop novel, rigorous techniques, to calculate refined measures of quantum entanglement of spatial regions in conformal field theories with boundaries (BCFTs) at large central charge, in thermal and “locally quenched” non-thermal initial states.

At large central charge, BCFT correlators that compute measures of quantum information are expected to undergo a sharp transition (as a function of the size of spatial regions). This is due to a switch in dominance between intermediate exchanges involving bulk primary states to intermediate exchanges of boundary states.

A major goal will be to make precise this qualitative picture within the framework of “generalized free fields” which have recently been proposed as the appropriate CFT construct to describe strongly coupled CFTs possessing holographic gravity duals. Little is known about interacting BCFT n-point functions. Our investigation will reveal new general features of BCFT entanglement measures at strong coupling.

A deep physical interpretation of the BCFT system has in recent months been at the epicentre of one of the most important advances in theoretical physics made in recent times (Nov 2019):

Holographic duality relates a BCFT to the same CFT propagating in the near horizon geometry of a black hole dual to the boundary degrees of freedom. Thus BCFT measures of entanglement get related to quantum entanglement entropies of subsets of Hawking radiation emitted by the black hole!

The transition between the two regimes of BCFT correlators is precisely what resolves the celebrated information loss paradox for black holes posed by Hawking. In the gravity picture the transition is between the usual black hole geometry and a new semiclassical wormhole saddle-point.

Remarkably, the wormhole geometry identifies the black hole interior with the Hawking radiation outside and reproduces the celebrated “Page curve” for the entanglement entropy of Hawking radiation required by unitarity of Quantum Mechanics.

Our goal is to understand how the black hole interior degrees of freedom are encoded in the Hawking radiation. We can extract this from strongly coupled bCFT correlators modelled by generalised free fields. We will also compare and contrast these fine-grained correlations against our previous results for weakly coupled CFTs propagating in the black hole background.

The question raised above is perhaps the single most pressing one in the effort to pick apart the complexity of the quantum state of the Hawking radiation emitted by a black hole and how universal its detailed properties are.

The inclusion of wormhole saddles in the gravitational partition function, instrumental in resolving the information loss paradox, leads to a beautiful interpretation of the gravitational description of the system: it is a sum of partition functions of the so-called 2d JT gravity defined over surfaces of arbitrary genus and arbitrary number of boundaries. Remarkably these correspond to the genus expansion of certain matrix integrals. It remains a fascinating question to understand how such a genus expansion is encoded in BCFT correlators, one which we expect to be able to attack in the final stages of the project.

The questions we plan to address are topical and yet largely unexplored. The Swansea team consists of world leading experts (TJH, DT, SPK ) in holography, string theory and QFT (BL) and has already produced publications in closely related directions and continues to pursue this research vigorously.


Candidates must have a First, Upper Second Class Honours or a Master’s degree with Merit, in a relevant discipline.

For candidates whose first language is not English, we require IELTS 6.5 (with 6.0 in each component) or equivalent. Please visit our website for a list of acceptable English language tests. We prefer candidates to have already met the English Language requirements at the point of application, although this is not a requirement.

This scholarship is open to UK and international candidates. Please note, international and EU students may have to pay the difference between the home (UK) UKRI fee and the institutional international student fee.

NB: If you are holding a non-UK degree, please see Swansea University degree comparisons to find out if you meet the eligibility. 

If you have any questions regarding your academic eligibility based on the above comparison, please email [Email Address Removed] with the web-link to the scholarship(s) you are interested in. 

Funding Notes

This three-year fully funded scholarship covers UK tuition fees and an annual stipend of £15,285.
Research Training Support Grant (RTSG) of £1,000 per annum covering travel and other research expenses is also provided.
This scholarship is open to UK and international candidates. Please note, international and EU students may have to pay the difference between the home (UK) UKRI fee and the institutional international student fee.
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