Higher-curvature Gravities from Braneworlds and the Holographic c-theorem

We study the structure of the higher-curvature gravitational densities that are induced from holographic renormalization in <math display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math>. In a braneworld construction, such densities define a <math display="inline"><mi>d</mi></math>-dimensional higher-curvature gravitational theory on the brane, which in turn is dual to a (<math display="inline"><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></math>)-dimensional CFT living at its boundary. We show that this <math display="inline"><mrow><msub><mrow><mi>CFT</mi></mrow><mrow><mi>d</mi><mo>-</mo><mn>1</mn></mrow></msub></mrow></math> satisfies a holographic <math display="inline"><mi>c</mi></math>-theorem in general dimensions (different than the <math display="inline"><mi>g</mi></math>-theorem of holographic boundary CFTs), since at each and every order the higher-curvature densities satisfy <math display="inline"><mi>c</mi></math>-theorems on their own. We find that, in these densities, the terms that affect the monotonicity of the holographic <math display="inline"><mi>c</mi></math>-function are algebraic in the curvature, and do not involve covariant derivatives of the Riemann tensor. We examine various other features of the holographically induced higher-curvature densities, such as the presence of reduced-order traced equations, and their connection to Born-Infeld-type gravitational Lagrangians.