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I will briefly explain my understanding on the subject.

In the following explanation i refer to the Poincarè group meaning the group:

$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin^+(1,3)$$

The standard model

To build the standard model we need 2 main ingredients:

• a global Poincarè group to build our fields as representations of such a group, scalars vectors 2-tensors spinors and all that.
• a gauge group, namely $SU(3)_C×SU(2)_L×U(1)_Y$, needed to obtain the interactions between the fields and have the charges.

I know that we also have a Higgs field which is not associated to a gauge group but is necessary to break the $SU(2)_L×U(1)_Y$ part and gain the masses through the Yukawa couplings.

We then build the fields using representations of a global Poincarè and the local gauge groups and we build the usual standard model action with kinetic terms (with covariant derivatives), theta terms, Yukawa terms and the Higgs potential.

Gravity in a gauge theory form

The classical General Relativity is built on two key arguments:

1. Locally it is always possible to choose a locally inertial frame (LIF)

2. The connection is the torsion free one$^1$

From such assumptions you can built the usual gravitational action and the coupling to matter via the covariant derivative and the metric.

It is also possible to build gravity as a gauge theory.

Taking as gauge group the Poincarè group, you build a connection on the principal bundle which is composed of a translational gauge field, the tetrad field $e$ and a rotational gauge field, the spin connection $\omega$.

Each of this two fields has its own curvature tensor: $R^{(e)}$ and $R^{(\omega)}$. Imposing the choice of a torsion free connection give rise to the so called soldering equation, which states that $R^{(e)}=0$, and makes possible to obtain the spin connection out of the tetrad, as in classical GR you obtain the Levi-Civita connection from the metric.

After setting the translational curvature tensor to zero one recovers the action of classical general relativity but with the new variables.

Since this is now a gauge theory one uses the Poincarè connection to build the covariant derivate for matter fields, and this is what is done usually in quantum field theory over curved background spacetimes.

Question:

Since we already know that the standard model is built upon Poincarè representations, why can't we incorporate into the standard model the gravitational interaction gauging the Poincarè group, having then a $$G = \mathcal{P}_{1,3} × SU(3)_C×SU(2)_L ×U(1)_Y$$

gauge group?

I already know that gravity is not UV-complete, but neither is the standard model, so what is the reason to not use such a theory as our most complete effective theory up to some scale?

$^1$ Here i'm talking about the standard formulation of general relativity where the connection is the torsion free Levi-Civita connection derived from the metric, not the indipendent affine connection of the Palatini formulation

I will briefly explain my understanding on the subject.

In the following explanation i refer to the Poincarè group meaning the group:

$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin^+(1,3)$$

The standard model

To build the standard model we need 2 main ingredients:

• a global Poincarè group to build our fields as representations of such a group, scalars vectors 2-tensors spinors and all that.
• a gauge group, namely $SU(3)_C×SU(2)_L×U(1)_Y$, needed to obtain the interactions between the fields and have the charges.

I know that we also have a Higgs field which is not associated to a gauge group but is necessary to break the $SU(2)_L×U(1)_Y$ part and gain the masses through the Yukawa couplings.

We then build the fields using representations of a global Poincarè and the local gauge groups and we build the usual standard model action with kinetic terms (with covariant derivatives), theta terms, Yukawa terms and the Higgs potential.

Gravity in a gauge theory form

The classical General Relativity is built on two key arguments:

1. Locally it is always possible to choose a locally inertial frame (LIF)

2. The connection is the torsion free one$^1$

From such assumptions you can built the usual gravitational action and the coupling to matter via the covariant derivative and the metric.

It is also possible to build gravity as a gauge theory.

Taking as gauge group the Poincarè group, you build a connection on the principal bundle which is composed of a translational gauge field, the tetrad field $e$ and a rotational gauge field, the spin connection $\omega$.

Each of this two fields has its own curvature tensor: $R^{(e)}$ and $R^{(\omega)}$. Imposing the choice of a torsion free connection give rise to the so called soldering equation, which states that $R^{(e)}=0$ in vacuum, and makes possible to obtain the spin connection out of the tetrad, as in classical GR you obtain the Levi-Civita connection from the metric.

After setting the translational curvature tensor to zero one recovers the action of classical general relativity but with the new variables.

Principle (1) tells us that locally the metric is always Minkowsky, so combining this with the fact that now this is a gauge theory, one uses the Poincarè connection to build the covariant derivate for matter fields. We have a (classical) theory which encompass all the interactions using the gauge formalism machinery.

It becomes QFT on curved spacetime once one fixes the classical Poincarè solution to a specific $(e_0,\omega_0)$ and quantize the remaining fields.

Question:

Since we already know that the standard model is built upon Poincarè representations, why can't we incorporate into the standard model the gravitational interaction gauging the Poincarè group, having then a $$G = \mathcal{P}_{1,3} × SU(3)_C×SU(2)_L ×U(1)_Y$$

gauge group?

I already know that gravity is probably not UV-complete, but neither is the standard model, so what is the reason to not use such a theory as our most complete effective theory up to some scale?

I know that at low energies gravitational interactions are negligible, and that we cannot do high energy perturbation theory, but perturbation theory is not a necessity of natural laws but rather a useful tool for us when we are not able to exactly solve equations.

So what is the reason to not say that the standard model + Poincarè gauge theory is a (UV-incomplete) quantum theory of all interactions?

$^1$ Here i'm talking about the standard formulation of general relativity where the connection is the torsion free Levi-Civita connection derived from the metric.

I will briefly explain my understanding on the subject.

In the following explanation i refer to the Poincarè group meaning the group:

$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin(1,3)$$

The standard model

To build the standard model we need 2 main ingredients:

• a global Poincarè group to build our fields as representations of such a group, scalars vectors 2-tensors spinors and all that.
• a gauge group, namely $SU(3)_C×SU(2)_L×U(1)_Y$, needed to obtain the interactions between the fields and have the charges.

I know that we also have a Higgs field which is not associated to a gauge group but is necessary to break the $SU(2)_L×U(1)_Y$ part and gain the masses through the Yukawa couplings.

We then build the fields using representations of a global Poincarè and the local gauge groups and we build the usual standard model action with kinetic terms (with covariant derivatives), theta terms, Yukawa terms and the Higgs potential.

Gravity in a gauge theory form

The classical General Relativity is built on two key arguments:

1. Locally it is always possible to choose a locally inertial frame (LIF)

2. The connection is the torsion free one$^1$

From such assumptions you can built the usual gravitational action and the coupling to matter via the covariant derivative and the metric.

It is also possible to build gravity as a gauge theory.

Taking as gauge group the Poincarè group, you build a connection on the principal bundle which is composed of a translational gauge field, the tetrad field $e$ and a rotational gauge field, the spin connection $\omega$.

Each of this two fields has its own curvature tensor: $R^{(e)}$ and $R^{(\omega)}$. Imposing the choice of a torsion free connection give rise to the so called soldering equation, which states that $R^{(e)}=0$, and makes possible to obtain the spin connection out of the tetrad, as in classical GR you obtain the Levi-Civita connection from the metric.

After setting the translational curvature tensor to zero one recovers the action of classical general relativity but with the new variables.

Since this is now a gauge theory one uses the Poincarè connection to build the covariant derivate for matter fields, and this is what is done usually in quantum field theory over curved background spacetimes.

Question:

Since we already know that the standard model is built upon Poincarè representations, why can't we incorporate into the standard model the gravitational interaction gauging the Poincarè group, having then a $$G = \mathcal{P}_{1,3} × SU(3)_C×SU(2)_L ×U(1)_Y$$

gauge group?

I already know that gravity is not UV-complete, but neither is the standard model, so what is the reason to not use such a theory as our most complete effective theory up to some scale?

$^1$ Here i'm talking about the standard formulation of general relativity where the connection is the torsion free Levi-Civita connection derived from the metric, not the indipendent affine connection of the Palatini formulation

I will briefly explain my understanding on the subject.

In the following explanation i refer to the Poincarè group meaning the group:

$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin^+(1,3)$$

The standard model

To build the standard model we need 2 main ingredients:

• a global Poincarè group to build our fields as representations of such a group, scalars vectors 2-tensors spinors and all that.
• a gauge group, namely $SU(3)_C×SU(2)_L×U(1)_Y$, needed to obtain the interactions between the fields and have the charges.

I know that we also have a Higgs field which is not associated to a gauge group but is necessary to break the $SU(2)_L×U(1)_Y$ part and gain the masses through the Yukawa couplings.

We then build the fields using representations of a global Poincarè and the local gauge groups and we build the usual standard model action with kinetic terms (with covariant derivatives), theta terms, Yukawa terms and the Higgs potential.

Gravity in a gauge theory form

The classical General Relativity is built on two key arguments:

1. Locally it is always possible to choose a locally inertial frame (LIF)

2. The connection is the torsion free one$^1$

From such assumptions you can built the usual gravitational action and the coupling to matter via the covariant derivative and the metric.

It is also possible to build gravity as a gauge theory.

Taking as gauge group the Poincarè group, you build a connection on the principal bundle which is composed of a translational gauge field, the tetrad field $e$ and a rotational gauge field, the spin connection $\omega$.

Each of this two fields has its own curvature tensor: $R^{(e)}$ and $R^{(\omega)}$. Imposing the choice of a torsion free connection give rise to the so called soldering equation, which states that $R^{(e)}=0$, and makes possible to obtain the spin connection out of the tetrad, as in classical GR you obtain the Levi-Civita connection from the metric.

After setting the translational curvature tensor to zero one recovers the action of classical general relativity but with the new variables.

Since this is now a gauge theory one uses the Poincarè connection to build the covariant derivate for matter fields, and this is what is done usually in quantum field theory over curved background spacetimes.

Question:

Since we already know that the standard model is built upon Poincarè representations, why can't we incorporate into the standard model the gravitational interaction gauging the Poincarè group, having then a $$G = \mathcal{P}_{1,3} × SU(3)_C×SU(2)_L ×U(1)_Y$$

gauge group?

I already know that gravity is not UV-complete, but neither is the standard model, so what is the reason to not use such a theory as our most complete effective theory up to some scale?

$^1$ Here i'm talking about the standard formulation of general relativity where the connection is the torsion free Levi-Civita connection derived from the metric, not the indipendent affine connection of the Palatini formulation

I will briefly explain my understanding on the subject.

The standard model

To build the standard model we need 2 main ingredients:

• a global Poincarè group to build our fields as representations of such a group, scalars vectors 2-tensors spinors and all that.
• a gauge group, namely $SU(3)_C×SU(2)_L×U(1)_Y$, needed to obtain the interactions between the fields and have the charges.

I know that we also have a Higgs field which is not associated to a gauge group but is necessary to break the $SU(2)_L×U(1)_Y$ part and gain the masses through the Yukawa couplings.

We then build the fields using representations of a global Poincarè and the local gauge groups and we build the usual standard model action with kinetic terms (with covariant derivatives), theta terms, Yukawa terms and the Higgs potential.

Gravity in a gauge theory form

The classical General Relativity is built on two key arguments:

1. Locally it is always possible to choose a locally inertial frame (LIF)

2. The connection is the torsion free one$^1$

From such assumptions you can built the usual gravitational action and the coupling to matter via the covariant derivative and the metric.

It is also possible to build gravity as a gauge theory.

Taking as gauge group the Poincarè group, you build a connection on the principal bundle which is composed of a translational gauge field, the tetrad field $e$ and a rotational gauge field, the spin connection $\omega$.

Each of this two fields has its own curvature tensor: $R^{(e)}$ and $R^{(\omega)}$. Imposing the choice of a torsion free connection give rise to the so called soldering equation, which states that $R^{(e)}=0$, and makes possible to obtain the spin connection out of the tetrad, as in classical GR you obtain the Levi-Civita connection from the metric.

After setting the translational curvature tensor to zero one recovers the action of classical general relativity but with the new variables.

Since this is now a gauge theory one uses the Poincarè connection to build the covariant derivate for matter fields, and this is what is done usually in quantum field theory over curved background spacetimes.

Question:

Since we already know that the standard model is built upon Poincarè representations, why can't we incorporate into the standard model the gravitational interaction gauging the Poincarè group, having then a $$G = ISO(1,3) × SU(3)_C×SU(2)_L ×U(1)_Y$$

gauge group?

I already know that gravity is not UV-complete, but neither is the standard model, so what is the reason to not use such a theory as our most complete effective theory up to some scale?

$^1$ Here i'm talking about the standard formulation of general relativity where the connection is the torsion free Levi-Civita connection derived from the metric, not the indipendent affine connection of the Palatini formulation

I will briefly explain my understanding on the subject.

In the following explanation i refer to the Poincarè group meaning the group:

$$\mathcal{P}_{1,3} = \mathbb{R}^{1,3} \rtimes Spin(1,3)$$

The standard model

To build the standard model we need 2 main ingredients:

• a global Poincarè group to build our fields as representations of such a group, scalars vectors 2-tensors spinors and all that.
• a gauge group, namely $SU(3)_C×SU(2)_L×U(1)_Y$, needed to obtain the interactions between the fields and have the charges.

I know that we also have a Higgs field which is not associated to a gauge group but is necessary to break the $SU(2)_L×U(1)_Y$ part and gain the masses through the Yukawa couplings.

We then build the fields using representations of a global Poincarè and the local gauge groups and we build the usual standard model action with kinetic terms (with covariant derivatives), theta terms, Yukawa terms and the Higgs potential.

Gravity in a gauge theory form

The classical General Relativity is built on two key arguments:

1. Locally it is always possible to choose a locally inertial frame (LIF)

2. The connection is the torsion free one$^1$

From such assumptions you can built the usual gravitational action and the coupling to matter via the covariant derivative and the metric.

It is also possible to build gravity as a gauge theory.

Taking as gauge group the Poincarè group, you build a connection on the principal bundle which is composed of a translational gauge field, the tetrad field $e$ and a rotational gauge field, the spin connection $\omega$.

Each of this two fields has its own curvature tensor: $R^{(e)}$ and $R^{(\omega)}$. Imposing the choice of a torsion free connection give rise to the so called soldering equation, which states that $R^{(e)}=0$, and makes possible to obtain the spin connection out of the tetrad, as in classical GR you obtain the Levi-Civita connection from the metric.

After setting the translational curvature tensor to zero one recovers the action of classical general relativity but with the new variables.

Since this is now a gauge theory one uses the Poincarè connection to build the covariant derivate for matter fields, and this is what is done usually in quantum field theory over curved background spacetimes.

Question:

Since we already know that the standard model is built upon Poincarè representations, why can't we incorporate into the standard model the gravitational interaction gauging the Poincarè group, having then a $$G = \mathcal{P}_{1,3} × SU(3)_C×SU(2)_L ×U(1)_Y$$

gauge group?

I already know that gravity is not UV-complete, but neither is the standard model, so what is the reason to not use such a theory as our most complete effective theory up to some scale?

$^1$ Here i'm talking about the standard formulation of general relativity where the connection is the torsion free Levi-Civita connection derived from the metric, not the indipendent affine connection of the Palatini formulation