de Sitter Vacua in the String Landscape: La Petite Version
453
the higher order quantum terms contribute to the cosmological constant? The answer
as detailed in [13] and [14] is easy to see: at higher orders in g s we also switch on
other G-flux components that appear at higher orders in k in eq. (2.5) of [14]. These
components back-react on the geometry creating negative gravitational potentials.
These negative gravitational potentials are then exactly cancelled by the positive
contributions from the quantum potential at higher orders in g s in such a way that
the zeroth order cosmological constant remains unaltered.
The final comment is on the possibility of realizing inflation on our set-up. It
has been claimed in [18] that warm inflation may indeed be outside the swampland.
Here however we want to comment on the possibility of using the time-dependences
to allow for some variant of the D3-D7 inflationary model of [19], the D7-branes
in IIB appearing from the orbifold points in M-theory and the D3-branes appearing
from the M2-branes that we require the cancel anomalies in the system. This of
course calls for a F-theory uplift of our IIB picture, so a natural question is to see
whether the M-theory and F-theory connection could be made more precise with
time-dependent internal degrees of freedom. It would also be interesting to compare
our answers with those of [20].
3 Discussion and Conclusion
In this short note we have summarized some of the contents of [13] and [14]
related to the possibility of the existence of four-dimensional effective field theory
description with de Sitter isometries and time-dependent internal degrees of freedom
in IIB. However there are still questions related to the exact meaning of Wilsonian
effective actions in such spaces, for example, how the time-dependent degrees of
freedom are integrated out, and whether the de Sitter solutions that we have could be
interpreted as vacua or coherent states over some supersymmetric solitonic minima.
Additionally, the precise connection to TCC needs to be spelled out, maybe along
the lines of the recent work [21]. All these and other advances show that this is
indeed an exciting time for cosmology.
References
1. S. Kachru, R. Kallosh, A.D. Linde, S.P. Trivedi, De Sitter vacua in string theory. Phys. Rev.
D 68, 046005 (2003). [hep-th/0301240]; C.P. Burgess, R. Kallosh, F. Quevedo, De Sitter
string vacua from supersymmetric D terms. J. High Energy Phys. 0310, 056 (2003). [hepth/0309187]; E. Silverstein, Simple de Sitter solutions. Phys. Rev. D 77, 106006 (2008).
[arXiv:0712.1196 [hep-th]]
2. I. Bena, M. Grana, S. Kuperstein, S. Massai, Anti-D3 branes: singular to the bitter end. Phys.
Rev. D 87(10), 106010 (2013). [arXiv:1206.6369 [hep-th]]; Polchinski-Strassler does not uplift
Klebanov-Strassler. J. High Energy Phys. 1309, 142 (2013) [arXiv:1212.4828 [hep-th]]
453
the higher order quantum terms contribute to the cosmological constant? The answer
as detailed in [13] and [14] is easy to see: at higher orders in g s we also switch on
other G-flux components that appear at higher orders in k in eq. (2.5) of [14]. These
components back-react on the geometry creating negative gravitational potentials.
These negative gravitational potentials are then exactly cancelled by the positive
contributions from the quantum potential at higher orders in g s in such a way that
the zeroth order cosmological constant remains unaltered.
The final comment is on the possibility of realizing inflation on our set-up. It
has been claimed in [18] that warm inflation may indeed be outside the swampland.
Here however we want to comment on the possibility of using the time-dependences
to allow for some variant of the D3-D7 inflationary model of [19], the D7-branes
in IIB appearing from the orbifold points in M-theory and the D3-branes appearing
from the M2-branes that we require the cancel anomalies in the system. This of
course calls for a F-theory uplift of our IIB picture, so a natural question is to see
whether the M-theory and F-theory connection could be made more precise with
time-dependent internal degrees of freedom. It would also be interesting to compare
our answers with those of [20].
3 Discussion and Conclusion
In this short note we have summarized some of the contents of [13] and [14]
related to the possibility of the existence of four-dimensional effective field theory
description with de Sitter isometries and time-dependent internal degrees of freedom
in IIB. However there are still questions related to the exact meaning of Wilsonian
effective actions in such spaces, for example, how the time-dependent degrees of
freedom are integrated out, and whether the de Sitter solutions that we have could be
interpreted as vacua or coherent states over some supersymmetric solitonic minima.
Additionally, the precise connection to TCC needs to be spelled out, maybe along
the lines of the recent work [21]. All these and other advances show that this is
indeed an exciting time for cosmology.
References
1. S. Kachru, R. Kallosh, A.D. Linde, S.P. Trivedi, De Sitter vacua in string theory. Phys. Rev.
D 68, 046005 (2003). [hep-th/0301240]; C.P. Burgess, R. Kallosh, F. Quevedo, De Sitter
string vacua from supersymmetric D terms. J. High Energy Phys. 0310, 056 (2003). [hepth/0309187]; E. Silverstein, Simple de Sitter solutions. Phys. Rev. D 77, 106006 (2008).
[arXiv:0712.1196 [hep-th]]
2. I. Bena, M. Grana, S. Kuperstein, S. Massai, Anti-D3 branes: singular to the bitter end. Phys.
Rev. D 87(10), 106010 (2013). [arXiv:1206.6369 [hep-th]]; Polchinski-Strassler does not uplift
Klebanov-Strassler. J. High Energy Phys. 1309, 142 (2013) [arXiv:1212.4828 [hep-th]]