# Emergent Strings at an Infinite Distance with Broken Supersymmetry

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Brane Dynamics and Weak Gravity

## 3. Bubble Nucleation and Holography

#### Emergent Supersymmetry and WZW Cosets

## 4. Infinite Distances and Emergent Strings

#### 4.1. Graviton Vertex from Brane Separation

#### 4.2. Anomalous Dimensions of Scalar Operators

#### 4.3. Anomalous Dimensions of Higher-Spin Currents

## 5. Conclusions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | |

2 | |

3 | See also [48] for a T-dual version of this construction. |

4 | The role of fermions in geometries of this type has been studied in [49]. |

5 | |

6 | |

7 | Normally, $\alpha $ has dimensions of squared length. In order to keep (21) free of unnecessary clutter, we work in string units for the ${X}^{i}$, so that $\alpha $ is dimensionless. |

8 | The same results can be obtained with other regularizations. |

9 | Let us remark that the UV “lattice” cutoff a is always implied in these expressions, since the base of general exponentials is to be dimensionless. |

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**Figure 1.**A heavy stack of D1-branes (in the orientifold models) or NS5-branes (in the heterotic model) sources a spacetime geometry whose near-horizon limit is an $\mathrm{AdS}\times S$ throat [37,45]. One can expect branes on conical singularities to produce similar Freund–Rubin compactifications in this limit.

**Figure 2.**The interaction between branes in the presence of string-scale supersymmetry breaking is mediated by the gravitational tadpole. As as a result, the effective charge-to-tension ratio is renormalized by a $\mathcal{O}\left(1\right)$ factor, and like-charge branes exert mutually repulsive forces [37,45].

**Figure 3.**The proposed holographic dual of the cascade of flux tunneling processes in the gravitational EFT is an RG flow in the boundary field theory [71]. Depending on the size, location and number of nucleation events, the trajectory can vary, approaching different fixed points. As $N\gg 1$ increases, the flows ought to approach the fixed points more closely, since the dual $\mathrm{AdS}$ vacua are closer to stability [45].

**Figure 4.**The fixed points approached by the holographic RG flow can arise from the IR dynamics of the worldvolume gauge theory living on D1-brane stacks. The final state corresponds to the IR dynamics of a single D1-brane, which features a free sector with conserved single-trace higher-spin currents dual to massless single-particle higher-spin states. Furthermore, the Sugimoto model of [28] features emergent supersymmetry on account of $\mathrm{Spin}\left(8\right)$ triality.

**Figure 5.**The IR dynamics of the worldvolume gauge theories living on $N=2$ and $N=1$ D1-branes can be described via NL$\sigma $M and WZW coset constructions. The RG flow connecting the corresponding CFTs is triggered by the target-space metric, which is marginally irrelevant in the IR and yields an infinite distance along the flow.

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**MDPI and ACS Style**

Basile, I.
Emergent Strings at an Infinite Distance with Broken Supersymmetry. *Astronomy* **2023**, *2*, 206-225.
https://doi.org/10.3390/astronomy2030015

**AMA Style**

Basile I.
Emergent Strings at an Infinite Distance with Broken Supersymmetry. *Astronomy*. 2023; 2(3):206-225.
https://doi.org/10.3390/astronomy2030015

**Chicago/Turabian Style**

Basile, Ivano.
2023. "Emergent Strings at an Infinite Distance with Broken Supersymmetry" *Astronomy* 2, no. 3: 206-225.
https://doi.org/10.3390/astronomy2030015