Cumrun Vafa discusses the string landscape and the swampland in string theory. He argues that the vast number of string vacua is not as extensive as allowed by consistent-looking effective field theories. Instead, there exists a larger swampland of effective field theories that appear consistent but are actually inconsistent. The boundary of the landscape is a central question related to the universality of quantum gravitational theories.
The paper explores finiteness criteria as a key factor in identifying this boundary. These criteria include the finiteness of scalar field moduli space, the number of matter fields, and the rank of gauge groups. These properties are directly related to the consistency of quantum gravity coupled to matter. In string theory, these finiteness properties are non-trivial and are deeply connected to string dualities, including S-dualities.
The finiteness of scalar field moduli space is discussed in the context of string theory compactifications. For example, in type IIB theory, the scalar field space is finite due to S-duality. Similarly, compactifications on Calabi-Yau manifolds and other geometries show that the scalar field moduli space is finite. This finiteness is also related to the non-zero Newton's constant in the gravitational sector.
The finiteness of matter fields is also discussed, with the number of matter fields bounded by the dimension of the cohomology of the compactification manifold. In string theory, the cohomology of the manifold is finite, leading to a finite number of matter fields. This finiteness is again related to the non-zero Newton's constant.
The paper also discusses restrictions on gauge fields, noting that certain gauge groups are more restricted in string theory than expected from semiclassical consistency. Examples include gauge groups with large ranks, which are not easily constructible in string theory.
The paper concludes that understanding these finiteness criteria is crucial for understanding string theory and what it means for a consistent quantum theory of gravity coupled to matter. It suggests that string theory can serve as a testing ground for proposed consistency conditions. The paper also highlights the importance of identifying general patterns of what is not possible to construct within string theory, despite being naively allowed as consistent effective theories.Cumrun Vafa discusses the string landscape and the swampland in string theory. He argues that the vast number of string vacua is not as extensive as allowed by consistent-looking effective field theories. Instead, there exists a larger swampland of effective field theories that appear consistent but are actually inconsistent. The boundary of the landscape is a central question related to the universality of quantum gravitational theories.
The paper explores finiteness criteria as a key factor in identifying this boundary. These criteria include the finiteness of scalar field moduli space, the number of matter fields, and the rank of gauge groups. These properties are directly related to the consistency of quantum gravity coupled to matter. In string theory, these finiteness properties are non-trivial and are deeply connected to string dualities, including S-dualities.
The finiteness of scalar field moduli space is discussed in the context of string theory compactifications. For example, in type IIB theory, the scalar field space is finite due to S-duality. Similarly, compactifications on Calabi-Yau manifolds and other geometries show that the scalar field moduli space is finite. This finiteness is also related to the non-zero Newton's constant in the gravitational sector.
The finiteness of matter fields is also discussed, with the number of matter fields bounded by the dimension of the cohomology of the compactification manifold. In string theory, the cohomology of the manifold is finite, leading to a finite number of matter fields. This finiteness is again related to the non-zero Newton's constant.
The paper also discusses restrictions on gauge fields, noting that certain gauge groups are more restricted in string theory than expected from semiclassical consistency. Examples include gauge groups with large ranks, which are not easily constructible in string theory.
The paper concludes that understanding these finiteness criteria is crucial for understanding string theory and what it means for a consistent quantum theory of gravity coupled to matter. It suggests that string theory can serve as a testing ground for proposed consistency conditions. The paper also highlights the importance of identifying general patterns of what is not possible to construct within string theory, despite being naively allowed as consistent effective theories.