## Final Report Summary - STRING-QCD-BH (String Theory, QCD and Black Holes)

String theory is a quantum theory of gravity, and has had several astounding successes in describing properties of black holes. Recent progress in string theory points to the possibility that black holes should not be thought of as fundamental objects, but rather as statistical descriptions of a huge number of smooth horizonless microstate geometries, or fuzzballs. If correct, this “fuzzball proposal” will revolutionize our understanding of black holes and quantum gravity in general: the classical black hole solution would be like the analogue of the

thermodynamic description of a gas, while the horizonless microstates would be the analogue of the statistical description of this gas.

Establishing this requires the construction and counting of very large classes of solutions that have the same charges, mass and angular momentum as a black hole, but have no horizon. We have been attacking this problem in the context of supergravity theories that emerge as low-energy limits of string theory, and we have constructed the largest known class of such solutions, parameterized by a continuous function of one variable, and hence an infinite number of parameters. We have also found evidence that there should exist even more complicated solutions parameterized by a function of two variables, whose entropy matches the entropy of the black hole. We have just succeeded in building some of these solutions explicitly, which is very strong evidence that this picture of black holes is correct.

In order to obtain the real world from string theory one needs to compactify it on certain six-dimensional spaces with flux. These flux compactifications generically produce Anti-deSitter (AdS) vacua, which have a negative cosmological constant and hence cannot describe our universe (which has a small positive cosmological constant). In a groundbreaking paper, Kachru, Kallosh, Linde and Trivedi proposed a way to bypass this problem by adding to flux compactifications branes that have a charge opposite to that of the flux (anti-D3 branes). These branes can then lift the negative cosmological constant to a small positive one, in the range one finds in our universe. This mechanism predicts that string theory has a landscape of possible deSitter (dS) vacua, and our universe is but one in this multitude (~10^500) of possible universes (also known as Multiverse). The problem with this is that string theory appears to lose predictability – the only explanation why our universe is the way it is becomes anthropic – and the longstanding hope of explaining all the physical laws of our universe from one unified framework becomes but a distant dream.

The PI and his collaborators have begun a research programme aimed at better understanding the uplift of AdS vacua to dS vacua via anti-D3 branes. We have constructed the solutions corresponding to anti-D3 branes in certain flux backgrounds, and have shown that all anti-D3 brane solutions must have a certain singularity. If this singularity is not physical (and so far all evidence points in this direction), then anti-D3 branes cannot be used to obtain dS vacua from AdS ones, and this in turn indicates that is is very likely that string theory does not have a landscape of deSitter vacua. This would re-launch the search for a mechanism to uplift AdS vacua and obtain deSitter vacua in string theory, and may restore the predictability of string theory.

thermodynamic description of a gas, while the horizonless microstates would be the analogue of the statistical description of this gas.

Establishing this requires the construction and counting of very large classes of solutions that have the same charges, mass and angular momentum as a black hole, but have no horizon. We have been attacking this problem in the context of supergravity theories that emerge as low-energy limits of string theory, and we have constructed the largest known class of such solutions, parameterized by a continuous function of one variable, and hence an infinite number of parameters. We have also found evidence that there should exist even more complicated solutions parameterized by a function of two variables, whose entropy matches the entropy of the black hole. We have just succeeded in building some of these solutions explicitly, which is very strong evidence that this picture of black holes is correct.

In order to obtain the real world from string theory one needs to compactify it on certain six-dimensional spaces with flux. These flux compactifications generically produce Anti-deSitter (AdS) vacua, which have a negative cosmological constant and hence cannot describe our universe (which has a small positive cosmological constant). In a groundbreaking paper, Kachru, Kallosh, Linde and Trivedi proposed a way to bypass this problem by adding to flux compactifications branes that have a charge opposite to that of the flux (anti-D3 branes). These branes can then lift the negative cosmological constant to a small positive one, in the range one finds in our universe. This mechanism predicts that string theory has a landscape of possible deSitter (dS) vacua, and our universe is but one in this multitude (~10^500) of possible universes (also known as Multiverse). The problem with this is that string theory appears to lose predictability – the only explanation why our universe is the way it is becomes anthropic – and the longstanding hope of explaining all the physical laws of our universe from one unified framework becomes but a distant dream.

The PI and his collaborators have begun a research programme aimed at better understanding the uplift of AdS vacua to dS vacua via anti-D3 branes. We have constructed the solutions corresponding to anti-D3 branes in certain flux backgrounds, and have shown that all anti-D3 brane solutions must have a certain singularity. If this singularity is not physical (and so far all evidence points in this direction), then anti-D3 branes cannot be used to obtain dS vacua from AdS ones, and this in turn indicates that is is very likely that string theory does not have a landscape of deSitter vacua. This would re-launch the search for a mechanism to uplift AdS vacua and obtain deSitter vacua in string theory, and may restore the predictability of string theory.