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K. Dasgupta et al.
that the swampland criteria of [7] are in fact inconsistent with simple models
of quintessence. More general arguments against swampland criteria themselves
have also been raised mostly concerning their implications on cosmology (see, for
example, [9]), or their implications on general effective field theories [10]. The latter
paper in fact questioned the ad hoc nature of the criteria themselves. As a response
to these objections, in [11], the criteria were given a slightly formal derivation using
the trans-Planckian problems first raised for inflationary cosmology in [12]. The
original swampland criteria of [7] are then elevated to a Trans-Planckian Censorship
Conjecture (TCC), meaning that the validity of the criteria [7] rely on censoring the
trans-Planckian modes in a theory of quantum gravity because these modes have
non-unitary evolutions. Whether this is really a problem in string theory, where we
expect a well-defined behavior at short distances, remains to be seen.
In this review, which basically summarizes some parts of [13] and [14], we
will argue that if the internal degrees of freedom in a type IIB compactification
with four-dimensional de Sitter isometries remain time-independent, then there is
no four-dimensional effective field theory description possible. Such backgrounds
may truly be in the swampland, thus providing some credence to [7]. However once
the internal degrees of freedom become time-dependent (but preserving the fourdimensional Newton constant), then an effective field theory description becomes
possible.
2 How Hard Is to Get a de Sitter Vacuum in String Theory?
Let us consider two sets of backgrounds: one, in which we allow a four-dimensional
de Sitter space with a flat slicing and an internal six-dimensional compact space with
time-independent warp-factors; and two, a similar compactification but now with an
internal six-dimensional space with time-dependent warp-factors. Additionally, for
the first case we allow all internal degrees of freedom to be time-independent (the
internal degrees of freedom being the three and five-form fluxes; as well as the axiodilaton), whereas for the second case we allow all internal degrees of freedom to
be time-dependent. In both cases however we keep vanishing axion but constant
dilaton. Question is which of these two backgrounds would solve the equations of
motion in type IIB theory?
In the absence of quantum corrections, even if we allow fluxes, branes, antibranes, and/or orientifold planes, neither of the two backgrounds can solve the sugra
equations of motion as was shown in [15] and [16]. This is of course a consequence
of the no-go theorem first proposed in [17]. The situation becomes more interesting
when quantum corrections are added in. The naive expectation would be that once
a sufficient number of quantum terms are added in, either of the two backgrounds
should solve the equations of motion. Unfortunately this expectation did not quite
turn out to be correct as was first demonstrated in [16] and [13]. In the absence
of time-dependent internal degrees of freedom, the equations of motion can never
be solved because the quantum corrections do not lead to an effective field theory
K. Dasgupta et al.
that the swampland criteria of [7] are in fact inconsistent with simple models
of quintessence. More general arguments against swampland criteria themselves
have also been raised mostly concerning their implications on cosmology (see, for
example, [9]), or their implications on general effective field theories [10]. The latter
paper in fact questioned the ad hoc nature of the criteria themselves. As a response
to these objections, in [11], the criteria were given a slightly formal derivation using
the trans-Planckian problems first raised for inflationary cosmology in [12]. The
original swampland criteria of [7] are then elevated to a Trans-Planckian Censorship
Conjecture (TCC), meaning that the validity of the criteria [7] rely on censoring the
trans-Planckian modes in a theory of quantum gravity because these modes have
non-unitary evolutions. Whether this is really a problem in string theory, where we
expect a well-defined behavior at short distances, remains to be seen.
In this review, which basically summarizes some parts of [13] and [14], we
will argue that if the internal degrees of freedom in a type IIB compactification
with four-dimensional de Sitter isometries remain time-independent, then there is
no four-dimensional effective field theory description possible. Such backgrounds
may truly be in the swampland, thus providing some credence to [7]. However once
the internal degrees of freedom become time-dependent (but preserving the fourdimensional Newton constant), then an effective field theory description becomes
possible.
2 How Hard Is to Get a de Sitter Vacuum in String Theory?
Let us consider two sets of backgrounds: one, in which we allow a four-dimensional
de Sitter space with a flat slicing and an internal six-dimensional compact space with
time-independent warp-factors; and two, a similar compactification but now with an
internal six-dimensional space with time-dependent warp-factors. Additionally, for
the first case we allow all internal degrees of freedom to be time-independent (the
internal degrees of freedom being the three and five-form fluxes; as well as the axiodilaton), whereas for the second case we allow all internal degrees of freedom to
be time-dependent. In both cases however we keep vanishing axion but constant
dilaton. Question is which of these two backgrounds would solve the equations of
motion in type IIB theory?
In the absence of quantum corrections, even if we allow fluxes, branes, antibranes, and/or orientifold planes, neither of the two backgrounds can solve the sugra
equations of motion as was shown in [15] and [16]. This is of course a consequence
of the no-go theorem first proposed in [17]. The situation becomes more interesting
when quantum corrections are added in. The naive expectation would be that once
a sufficient number of quantum terms are added in, either of the two backgrounds
should solve the equations of motion. Unfortunately this expectation did not quite
turn out to be correct as was first demonstrated in [16] and [13]. In the absence
of time-dependent internal degrees of freedom, the equations of motion can never
be solved because the quantum corrections do not lead to an effective field theory