Research Vision

Two Hypotheses

It is important to separate two statements that are often compressed into one.

Hypothesis A

The complete massless sector \(\{g_{\mu\nu}, B_{\mu\nu}, \phi\}\) is irreducibly gravitational.

This is the starting hypothesis. It says that the metric, two-form, and dilaton should not be regarded as a metric plus auxiliary matter fields. They should be regarded as components of a single gravitational structure associated with closed strings.

Hypothesis A does not yet name the correct geometry. It only fixes the object that the geometry must describe.

Hypothesis B

Double Field Theory is the natural geometric theory describing the entire sector \(\{g_{\mu\nu}, B_{\mu\nu}, \phi\}\).

This is the working hypothesis.

The research program exists to establish or reject Hypothesis B. It is not enough to show that Double Field Theory is consistent, elegant, or useful. One must ask whether it is the geometry forced upon us when Hypothesis A is taken seriously.

The distinction matters. Hypothesis A identifies the gravitational multiplet. Hypothesis B proposes its geometry.

The Logical Gap

Closed string theory gives the multiplet \(\{g_{\mu\nu}, B_{\mu\nu}, \phi\}\).

General Relativity geometrizes \(g_{\mu\nu}\).

Between these statements lies a gap:

What geometry describes the full closed-string gravitational multiplet?

This is the place where Double Field Theory enters. It does not enter as an alternative formalism for familiar equations. It enters as the proposed answer to a missing geometric question.

If this answer is correct, then the usual Riemannian description is not discarded. It is recovered after choosing a Riemannian sector. In that sector, one obtains the standard variables of supergravity and, in appropriate limits, General Relativity.

Necessity as a Method

The research program should not proceed by listing definitions. It should proceed by asking what must exist if the working hypothesis is correct.

If Double Field Theory is gravity, it must possess its own geometry. Once geometry exists, it must possess its own metric data. Once metric data exist, one must define parallel transport. Once parallel transport exists, curvature becomes unavoidable. Once curvature exists, a variational principle becomes natural. Once a variational principle exists, a gravitational field equation becomes necessary.

Once a field equation exists, the theory must also describe propagation, matter coupling, phenomenology, and tests.

The value of a construction is measured by whether it occupies a necessary place in this chain.