Questions tagged [gauss-bonnet]

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Gauss-Bonnet topological invariant at linear order

I have a question about the Gauss-Bonnet invariant $T$, \begin{equation} T=R_{\mu\nu\alpha\beta}R^{\mu\nu\alpha\beta}-4R_{\mu\nu}R^{\mu\nu}+R^2 \end{equation} It is known that $T$ is a topological ...
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Variation of the Gauss-Bonnet term [closed]

We have the Gauss-Bonnet term $$L_{GB}=R^{2}-4R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$$ where $R$, $R_{\mu\nu}$ and $R_{\mu\nu\rho\sigma}$ are the Ricci scalar, the Ricci ...
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Graviton propagator, and Gauss-Bonnet gravity

Let's say we consider Einstein's Lagrangian from GR. In linearized gravity, we would expand the Ricci scalar to quadratic order in the perturbation parameter to find the propagator. My question is as ...
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1answer
102 views

Is the Palatini-Lovelock action of order $k$ topological in $2k$ dimensions?

I am interested in Lovelock actions in the metric-affine (or Palatini) formalism. It is well-known that the metric version (starting from the Levi-Civita curvature) of the Lovelock lagrangian of order ...
2
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1answer
164 views

What is the physical significance of Gaussian curvature in condensed matter physics?

In basic models concerning two-level systems, we deal with manifolds such as the Bloch sphere and torus. I believe that the Chern number is what dominates the theory in terms of ties to differential ...
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150 views

Euler charateristic of the universe

According to Gauss-Bonnet theorem, the volume integral $$\int_M d^4x\sqrt{-g}(R^{abcd}R_{abcd}-4R^{ab}R_{ab}+R^2)=\chi(M)$$ $\chi(M)$ is the Euler characteristic of the manifold $M$. Let us now ...
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How to show the Gauss-Bonnet term is a total derivative?

It is well-known that the Gauss-Bonnet term $$\mathcal L_G =R^2 -4 R_{\mu\nu}R^{\mu\nu}+R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\tag 1$$ do not contributes to equations of motion when adding it to ...
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173 views

$\langle TT\rangle$ correlator of the boundary CFT from metric fluctuations in the bulk gravity

Is there a reference which explains how the $\langle TT\rangle $ correlation of the boundary conformal field theory (CFT) can be holographically calculated from the bulk gravity? (..I am often getting ...
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788 views

Gauss-Bonnet term in Physics

Given a 4-dimensional compact manifold (torsion free), the Euler characteristic is defined as: $$E_4 ~=~ \int \epsilon_{abcd}R^{ab} \wedge R^{cd}$$ with $R^{ab}$ is the curvature 2-form. Perturb the ...
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2k views

Deriving Gauss-Bonnet Gravity (Or just higher order corrections)

I have been working for some time now on deriving the equations of motion (EOM) for the Gauss-Bonnet Gravity, which is given by the action: $$\int d^D x \sqrt{|g|} (R^2-4R_{ab}R^{ab}+R_{abcd}R^{abcd})...
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1answer
410 views

Euler number of the world sheet

I have a question in the section 3.2 "The Polyakov path integral" in Polchinski's string theory p. 83. Given $$ \chi=\frac{1}{4 \pi} \int_M d^2 \sigma g^{1/2} R + \frac{1}{2 \pi} \int_{\partial M}...
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1answer
384 views

Gauss-Bonnet theorem in the Hawking/Ellis book

At the page 336 of Hawking, Ellis: The Large Scale Structure of Space-Time, the Gauss-Bonnet theorem is stated as $$\int_H \hat{R}\ d\hat{S} = 2\pi \chi(H) \qquad (1)$$ with $$\hat{R} = R_{abcd} \...
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gauss-bonnet gravity constraints from string theory

recently there has been advances in observational constraints of gravity theories that contains scalars coupled to the gauss-bonnet topological term: http://arxiv.org/abs/0704.0175 http://arxiv.org/...