Evidence for F-Theory

Evidence for F-Theory

Feb. 1996 | Cumrun Vafa
This paper presents evidence for F-theory as a reformulation of type IIB string theory. The author constructs compact examples of D-manifolds for type IIB strings and shows that compactification of M-theory on a manifold with an elliptic fibration is equivalent to compactification of F-theory on $ K \times S^1 $. A large class of N = 1 theories in six dimensions is obtained by compactifying F-theory on Calabi-Yau threefolds. Compactifications of F-theory on $ Spin(7) $ holonomy manifolds down to four dimensions may provide a concrete realization of Witten's proposal for solving the cosmological constant problem. The paper discusses the 12-dimensional origin of type IIB theory, which is interpreted as an auxiliary manifold or as a real theory. The D-string, which has a gauge field on its worldsheet, has a critical dimension of 12 and lives in $ (10,2) $ space. The on-shell physical states only carry ten-dimensional momenta, while off-shell states may have more complex dependence on the extra two coordinates. The author considers compactifications of F-theory on K3, $ G_2 $ holonomy, and $ Spin(7) $ holonomy manifolds to 6, 5, and 4 dimensions, respectively. These compactifications lead to new type II vacua with N = 1 supersymmetry and gauge multiplets. Compactifications of F-theory on $ Spin(7) $ manifolds down to 4 dimensions apparently have no supersymmetry, but upon compactification to three dimensions, it is related to a supersymmetric M-theory. This may lead to a solution of the cosmological constant problem. The paper also discusses the duality between type IIB and F-theory, showing that the 8-dimensional solution is dual to the heterotic string compactification on $ T^2 $. The author argues that the 12-dimensional theory underlying type IIB is a natural extension of string theory, and that the D-string is dual to type IIB strings. The paper concludes that compactifications of F-theory on elliptic $ Spin(7) $ holonomy manifolds may provide a concrete realization of Witten's proposal for solving the cosmological constant problem.This paper presents evidence for F-theory as a reformulation of type IIB string theory. The author constructs compact examples of D-manifolds for type IIB strings and shows that compactification of M-theory on a manifold with an elliptic fibration is equivalent to compactification of F-theory on $ K \times S^1 $. A large class of N = 1 theories in six dimensions is obtained by compactifying F-theory on Calabi-Yau threefolds. Compactifications of F-theory on $ Spin(7) $ holonomy manifolds down to four dimensions may provide a concrete realization of Witten's proposal for solving the cosmological constant problem. The paper discusses the 12-dimensional origin of type IIB theory, which is interpreted as an auxiliary manifold or as a real theory. The D-string, which has a gauge field on its worldsheet, has a critical dimension of 12 and lives in $ (10,2) $ space. The on-shell physical states only carry ten-dimensional momenta, while off-shell states may have more complex dependence on the extra two coordinates. The author considers compactifications of F-theory on K3, $ G_2 $ holonomy, and $ Spin(7) $ holonomy manifolds to 6, 5, and 4 dimensions, respectively. These compactifications lead to new type II vacua with N = 1 supersymmetry and gauge multiplets. Compactifications of F-theory on $ Spin(7) $ manifolds down to 4 dimensions apparently have no supersymmetry, but upon compactification to three dimensions, it is related to a supersymmetric M-theory. This may lead to a solution of the cosmological constant problem. The paper also discusses the duality between type IIB and F-theory, showing that the 8-dimensional solution is dual to the heterotic string compactification on $ T^2 $. The author argues that the 12-dimensional theory underlying type IIB is a natural extension of string theory, and that the D-string is dual to type IIB strings. The paper concludes that compactifications of F-theory on elliptic $ Spin(7) $ holonomy manifolds may provide a concrete realization of Witten's proposal for solving the cosmological constant problem.
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