<p>The textbook N=1 supergravity has an F-term potential depending on a superpotential <i>W</i> (<i>z</i><sub><i>i</i></sub>) and a Kähler potential <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi>K</mi> <mfenced close=")" open="(" separators=","> <msup> <mi>z</mi> <mi>i</mi> </msup> <msup> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> <mover accent="true"> <mi>i</mi> <mo stretchy="true">¯</mo> </mover> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( K\left({z}^i,{\overline{z}}^{\overline{i}}\right) \)</EquationSource> </InlineEquation>, with the scalar potential <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi>V</mi> <mfenced close=")" open="(" separators=","> <msup> <mi>z</mi> <mi>i</mi> </msup> <msup> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> <mover accent="true"> <mi>i</mi> <mo stretchy="true">¯</mo> </mover> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( V\left({z}^i,{\overline{z}}^{\overline{i}}\right) \)</EquationSource> </InlineEquation> = <i>e</i><sup><i>K</i></sup>(|<i>DW</i>|<sup>2</sup> − 3|<i>W</i>|<sup>2</sup>). In this approach, it is not always easy to find the potential <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>V</mi> <mfenced close=")" open="(" separators=","> <msup> <mi>z</mi> <mi>i</mi> </msup> <msup> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> <mover accent="true"> <mi>i</mi> <mo stretchy="true">¯</mo> </mover> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( V\left({z}^i,{\overline{z}}^{\overline{i}}\right) \)</EquationSource> </InlineEquation> with the required properties. We show that in supergravity with a nilpotent superfield and <i>with any Kähler potential</i> <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi>K</mi> <mfenced close=")" open="(" separators=","> <msup> <mi>z</mi> <mi>i</mi> </msup> <msup> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> <mover accent="true"> <mi>i</mi> <mo stretchy="true">¯</mo> </mover> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( K\left({z}^i,{\overline{z}}^{\overline{i}}\right) \)</EquationSource> </InlineEquation> one can obtain <i>any desired potential</i> <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi>V</mi> <mfenced close=")" open="(" separators=","> <msup> <mi>z</mi> <mi>i</mi> </msup> <msup> <mover accent="true"> <mi>z</mi> <mo stretchy="true">¯</mo> </mover> <mover accent="true"> <mi>i</mi> <mo stretchy="true">¯</mo> </mover> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( V\left({z}^i,{\overline{z}}^{\overline{i}}\right) \)</EquationSource> </InlineEquation> by a proper choice of the Kähler metric of the nilpotent superfield. This construction is particularly suitable for cosmological and particle physics applications, which may require maximal freedom in the choice of kinetic terms and scalar potentials.</p>

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Streamlined supergravity

  • Renata Kallosh,
  • Andrei Linde

摘要

The textbook N=1 supergravity has an F-term potential depending on a superpotential W (zi) and a Kähler potential K z i z ¯ i ¯ \( K\left({z}^i,{\overline{z}}^{\overline{i}}\right) \) , with the scalar potential V z i z ¯ i ¯ \( V\left({z}^i,{\overline{z}}^{\overline{i}}\right) \) = eK(|DW|2 − 3|W|2). In this approach, it is not always easy to find the potential V z i z ¯ i ¯ \( V\left({z}^i,{\overline{z}}^{\overline{i}}\right) \) with the required properties. We show that in supergravity with a nilpotent superfield and with any Kähler potential K z i z ¯ i ¯ \( K\left({z}^i,{\overline{z}}^{\overline{i}}\right) \) one can obtain any desired potential V z i z ¯ i ¯ \( V\left({z}^i,{\overline{z}}^{\overline{i}}\right) \) by a proper choice of the Kähler metric of the nilpotent superfield. This construction is particularly suitable for cosmological and particle physics applications, which may require maximal freedom in the choice of kinetic terms and scalar potentials.