Jeong-Hyuck Park

박정혁 / 朴廷爀

Gravity of Closed Strings

My research centers on one question:

What is the gravitational theory naturally implied by
closed string theory?

Research is driven by questions, not by calculations.*

This question motivates the present research program, which investigates the generalized geometry naturally implied by the complete closed-string massless sector.

Research Vision

The question is not whether string theory contains gravity. It does.

Closed strings contain the universal massless gravitational sector \(\{g_{\mu\nu},B_{\mu\nu},\phi\}\).

General Relativity successfully geometrizes the metric.

The central question is therefore:

What geometry describes the complete closed-string gravitational sector?

Working Hypothesis Our current working hypothesis is that the gravitational theory naturally implied by closed string theory is Double Field Theory.

Unlike General Relativity, Double Field Theory is formulated in terms of the generalized metric \(\mathcal H_{AB}\) and the DFT dilaton \(d\), rather than an ordinary spacetime metric.

The familiar fields \(\{g_{\mu\nu},B_{\mu\nu},\phi\}\) arise only through a Riemannian parametrization of these fundamental fields.

More generally, the same formulation also admits genuinely non-Riemannian geometries.

Research Themes

Geometry

2010–

Geometry of the generalized metric, including doubled-yet-gauged spacetime and non-Riemannian geometry beyond General Relativity.
Beyond Riemannian geometry.

Unified Field Equation

2018–

Einstein Double Field Equation\(G_{AB}=T_{AB}\)A unified geometric equation for the universal massless sector of closed strings, coupling matter sources to its geometry. In a Riemannian parametrization, it governs the metric \(g_{\mu\nu}\), \(B\)-field \(B_{\mu\nu}\), and dilaton \(\phi\).
It also applies to non-Riemannian geometries.

The Einstein Double Field Equation

\[ G_{AB}=T_{AB}\,, \]

is formulated directly for the generalized metric \(\mathcal H_{AB}\) and the DFT dilaton \(d\), without assuming a Riemannian parametrization.

Whenever the generalized metric admits a Riemannian parametrization, the single \(\mathrm{O}(D,D)\)-covariant equation reproduces the following coupled equations for \(g_{\mu\nu}\), \(B_{\mu\nu}\), and \(\phi\):

\[ \begin{aligned} R_{\mu\nu}+2\trd_{\mu}(\partial_{\nu}\phi)-\quarter H_{\mu\rho\sigma}H_{\nu}{}^{\rho\sigma} &\;=\; K_{(\mu\nu)}\,,\\[0.7em] \half e^{2\phi}\trd^{\rho}\!\left(e^{-2\phi}H_{\rho\mu\nu}\right)&\;=\; K_{[\mu\nu]}\,,\\[0.7em] R+4\Box\phi-4\partial_{\mu}\phi\partial^{\mu}\phi-\textstyle{\frac{1}{12}}H_{\lambda\mu\nu}H^{\lambda\mu\nu}&\;=\; \To\,. \end{aligned} \]

For genuinely non-Riemannian generalized metrics, the same Einstein Double Field Equation remains well defined even though no ordinary invertible spacetime metric exists.

Read the Core Lecture Notes for further details.

Propagation

2025–

Universal propagation of all bosonic closed-string modes, including gravitational waves and higher-string excitations.
One propagation law for all bosonic closed-string modes.

Phenomenology

2022–

Post-Newtonian gravity, black holes, wormholes, cosmology without a conventional dark sector, and holography.
Toward observational tests of string gravity.

Where to Start

Step 1 Why?

Research Program

Overview of the question and direction.

Step 2 How?

Core Lecture Notes

Gravitational Core of Double Field Theory: Lecture Notes,
EPJC 2025.
A graduate-level introduction from the generalized metric to the Einstein Double Field Equation.

What is the gravitational theory naturally implied by closed string theory?

The program remains intentionally unfinished. Its future depends on the people who choose to work on it.

^*Bonus Question

Lab7616