# What is the physical significance of the dilaton in string theory?

Strings always have a dilaton in their spectrum. Its a scalar field (so presumably no spin), and so far a hypothetical particle. What is its physical significance?

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roughly speaking, it describes the (average?) scale of the compactification –  lurscher Jun 20 '12 at 22:39

The gravitational, massless, bosonic sector of the string effective action contains the metric tensor, and at least one more fundamental field φ, the dilaton. By comparing the Einstein’s (d+1) dimensional Einstein-Hilbert action with the effective tree level action mentioned before a relation between the effective string coupling (also fixing the G constant) and the dilaton field becomes manifest. The dilaton in string theory also can be rescaled to absorb trivial volume factors associated with compact spaces, but are also present in the non-compacted string models. The dilaton is a fundamental scalar field in closed string theory. The effective gravity equations in string theory includes the gravi-dilaton part that looks very similar to Brans-Dicke scalar-tensor theory of gravity (This is valid only at tree level). The dilaton field, as mention before, controls the string coupling constant so the genus expansion in string theory is directly related to the dilaton field and to corrections to General Relativity. There is also the possibility of a dilaton potential in noncritical dimensions. This creates the possibility that the dilaton field expectation value be fixed at a local minimum (probably in a non-perturbative regime), fixing the coupling between strings. The dilaton field is then an essential component of all superstrings models, and thus of the cosmological scenarios based on effective string actions. Chapter 9 in Maurizios Gasperini’s String Cosmology book is a very nice introduction to dilaton phenomenology and its importance in cosmology.

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In string theory, the dilaton field $\phi$ describes how strongly strings couple to one another. More precisely, in perturbation theory, the open string coupling constant is the exponential of the dilaton's expectation value $g_s = e^{\langle \phi\rangle}$.

The word dilaton is also used to refer to a quantum of the dilaton field. This is just a scalar particle.

In Kaluza-Klein theory, the word dilaton is sometimes used for the scalar field which arises when you compactify a metric, but the more word 'radion' is more standard; it's the diagonal component of the metric in the compactified direction. String theory mixes these ideas up to some degree. IIA string theory results from compactifying M-theory on a circle, and the dilaton field of IIA is the radion of M-theory on this circle.

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