Cumrun Vafa

Cumrun Vafa in his office at Harvard University

Cumrun Vafa ( Persian کامران وفا[ kɔːmˈrɔːn væˈfɔː ]; * August 1, 1960 in Tehran ) is an Iranian - American physicist and one of the leading string theorists .

Life

Cumrun Vafa attended Alborz High School in Tehran before going to the United States to study in 1977 . He received his bachelor's degree in math and physics from MIT in Cambridge in 1981 . He then went to Princeton University , where he completed his doctoral thesis under Edward Witten (subject: Symmetries, Inequalities and Index Theorems ) in 1985 . He has been an associate professor since 1988 and a professor at Harvard University since 1990 , where he started as a "Harvard Junior Fellow" in 1985 after completing his studies . Since 2003 he has been Donner Professor of Science at Harvard. In 1989 he received a research grant from the Alfred P. Sloan Foundation ( Sloan Research Fellowship ).

plant

His most important works include contributions to F-theory , topological string theory and (together with Andrew Strominger ) the microscopic description of the entropy of black holes via soliton solutions in superstring theory. One focus of his research is the connection between geometry and quantum field theories, which resulted in particular from the various string dualities (Geometric Engineering of Quantum Field Theories, 1997). He also made contributions to mirror symmetry in string theory and topological string theories when, with Rajesh Gopakumar, he introduced a new topological invariant in 1998 (Gopakumar-Vafa invariant), the BPS states of Calabi-Yau-3 varieties counts and has the form of a distribution function in a topological quantum field theory . They suspected (Gopakumar-Vafa conjecture) that the Gromow-Witten invariants of Calabi-Yau-3 varieties can be expressed by these Gopakumar-Vafa invariants.

Using topological string theory (a string theory model that is in some respects simpler than the superstring theory considered for realistic models), he also examined the connection with quantum gravity (topological gravity). In 1998 he and Gopakumar developed the view that topological string theories with closed strings (which describe gravity) are related to gauge field theories for high levels and that topological gravity in the model case of topological gauge field theories for these results in the limit case of large gauge groups (parameters ). The connection between gauge field theories and gravitation was already up -to- date in the context of the M-theory and the AdS / CFT correspondence , but the calculations were difficult. In 2004, together with Robbert Dijkgraaf and others , he proposed the topological M-theory as a unified theory of various shape theories of gravitation in different dimensions. ${\displaystyle SU(N)}$ ${\displaystyle N}$ ${\displaystyle N}$

The F-theory, which he introduced in 1996, allows the construction of new string vacuums by starting from a 12-dimensional theory that is compacted on the torus. This leads to an S-duality of the resulting IIB superstring theory. Instead of the torus, more general elliptically fibered manifolds M are used (i.e. the fibers have the structure of elliptical curves , topologically corresponding to a torus), whereby in superstring theory mostly Calabi-Yau manifolds are chosen for M , with four complex dimensions. From such and similar constructions, the realization arose in the 1990s that there is an abundance of possible string vacuums (which is referred to by the catchphrase landscape ). ${\displaystyle SL(2,\mathbb {Z} )}$

String landscapes and marshland

In order to limit the landscape consisting of the numerous possible string vacuums (string landscape), Vafa proposed in 2005 the search for physically convincing criteria that are suitable for excluding unphysical string vacuums (or false , unstable or metastable vacuums) (as swampland , Swampland). The idea of ​​this program was quickly adopted by string theorists.

In 2005 he presented with Nima Arkani-Hamed , Lubos Motl and Alberto Nicolis as such a possible criterion that gravity is always the weakest force (weak gravity conjecture) The hypothesis was also used in 2017 in the exclusion (cosmic censorship) of naked singularities in higher-dimensional ones Theories of gravitation.

In 2018, Vafa presented another wetland hypothesis ( De Sitter Wetland Conjecture ), which, if true, would exclude the usual string theory (with the cosmological predictions derived from it so far) and also represent a problem for the current inflation models of cosmology . According to the hypothesis, the vacuum energy density (expressed by a scalar potential in theories of quantum gravity) has to drop more than a limit given by (with a constant ). The discovery of dark energy in cosmology contradicts this as it corresponds to de-sitter universes with constant positive vacuum energy. According to Vafa's hypothesis, these do not belong to the landscape of possible string vacuums, but to the physically excluded marshland . In the possible universes, according to Vafa's de-sitter marshland conjecture, the vacuum energy must either decrease in accordance with the inequality given above or receive a stable negative value ( anti-de-sitter space ). In contrast to de-sitter universes, the latter are easy to construct in string theories (the difficulty of constructing de-sitter universes in string theories was a motive for Vafa's hypothesis). Dynamically changeable diminishing dark energy corresponds to quintessential models of dark energy. Astronomical observations on the dynamics of dark energy are in preparation ( Dark Energy Survey , the planned space telescope WFIRST , Euclid ) in order to decide on this hypothesis. Vafa's conjecture, however, also jeopardizes common cosmological inflation models, since it requires an excessively high rate of decrease in the energy of the inflation field . Vafa's hypothesis was controversial after its introduction and presentation at the Strings 2018 conference. ${\displaystyle V}$ ${\displaystyle |\nabla V|\geq cV}$ ${\displaystyle c}$

Honors

In 1998 he gave a plenary lecture at the International Congress of Mathematicians in Berlin ( Geometric Physics ). He has been a member of the American Academy of Arts and Sciences since 2005 and of the National Academy of Sciences since 2009 . In 2008 he received the Dirac Medal (ICTP) and in 2014 the Physics Frontiers Prize . For 2016 he was awarded the Dannie Heineman Prize for Mathematical Physics and for 2017 the Breakthrough Prize in Fundamental Physics . He is a fellow of the American Physical Society .

Fonts (selection)

In addition to the articles cited in the footnotes:

• with S. Kachru: Exact results for N = 2 compactifications of heterotic strings, Nucl. Phys. B 450, 1995, pp. 69-89, Arxiv
• with K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, R. Vakil, E. Zaslow: Mirror Symmetry, Clay Math. Monographs 1, AMS 2003
• with Andrew Neitzke: Topological strings and their physical applications , Arxiv 2004
• The string landscape and the swampland , Arxiv 2005
• Geometry and GUT , Arxiv 2009
• Puzzles to unravel the universe , 2020, ISBN 979-8642693636

Web links

• Cumrun Vafa's homepage
• Cumrun Vafa's publications at SPIRES
• Cumrun Vafa . In: arXiv.org
• Cumrun Vafa. American Institute of Physics(English). 

Individual evidence

1. ↑ Cumrun Vafa in the Mathematics Genealogy Project (English)
2. ↑ Strominger, Vafa Microscopic Origin of the Bekenstein-Hawking Entropy , Physical Letters B, Vol. 379, 1996, pp. 99-104, Arxiv
3. ^ Vafa, Sheldon Katz, Albrecht Klemm, Geometric Engineering of Quantum Field Theories , Nucl. Phys. B, Volume 497, 1997, pp. 173-195
4. ↑ Gopakumar, Vafa, M-Theory and topological strings, 2 parts, 1998, Arxiv, part 1 , Arxiv, part 2 ,
5. ^ Gopakumar, Vafa, On the Gauge Theory / Geometry Correspondence, Arxiv 1998
6. ↑ Gopakumar, Vafa, Topological Gravity as Large N Topological Gauge Theory, Adv. Theor. Math. Phys., Volume 2, 1998, pp. 413-442, Arxiv 1998
7. ^ Robbert Dijkgraaf, Sergei Gukov, Andrew Neitzke, Cumrun Vafa Topological M-theory as Unification of Form Theories of Gravity , Adv.Theor.Math.Phys., Volume 9, 2005, pp. 603-665
8. ^ Vafa, Evidence for F-Theory, Nucl. Phys. B, Volume 469, 1996, pp. 403-418, Arxiv
9. ^ Vafa, The String Landscape and the Swampland , 2005
10. ↑ T. Daniel Brennan, Federico Carta, Cumrun Vafa: The String Landscape, the Swampland, and the Missing Corner , review article based on the TASI lectures by Vafa 2017
11. ↑ Nima Arkani-Hamed, Lubos Motl, Alberto Nicolis, Cumrun Vafa: The String Landscape, Black Holes and Gravity as the Weakest Force , JHEP 0706: 060, 2007
12. ↑ Natalie Wolchover: Where Gravity Is Weak and Naked Singularities Are Verboten Quanta Magazine, June 20, 2017
13. ↑ Georges Obied, Hirosi Ooguri, Lev Spodyneiko, Cumrun Vafa: De Sitter space and the swampland. (pdf, 268 kB) In: Arxiv. July 17, 2018, accessed September 3, 2018 . Prateek Agrawal, Georges Obied, Paul J. Steinhardt, Cumrun Vafa: On the Cosmological Implications of the String Swampland. (pdf, 538 kB) In: Arxiv. July 19, 2018, accessed September 3, 2018 . Natalie Wolchover: Dark Energy May Be Incompatible With String Theory. In: Quanta Magazine. August 9, 2018, accessed September 3, 2018 . 
     
     
14. ↑ For de Sitter Universes, however, Shamit Kachru and colleagues suggested mechanisms in 2003 to still construct them in string theories, abbreviated to KKLT after the authors.
15. ^ Cumrun Vafa: Geometric Physics. (pdf, 262 kB) In: Arxiv. October 20, 1998, accessed September 3, 2018 .