De Sitter vacuum on nucleated D-branes with stringy corrections (2504.00600v1)

Abstract: We find four-dimensional de Sitter (dS) vacuum solutions on probe D-branes which nucleate in an asymptotically $\text{AdS}_5\times T^{1,1}$ background, including stringy corrections. A sufficiently high chemical potential induced by the wrapped D3-brane charge, breaking supersymmetry in the bulk, is essential to lead to the nucleation of the probe D-brane. We show that stringy corrections can yield a dS vacuum on a spherical D3-brane consistent with the observations without being fine-tuned. Motivated by the fact that the matter fields propagating in the compact extra dimensions can provide solutions for problems in particle physics and cosmology, we also construct a dS vacuum on a probe D5-brane which wraps on a two-torus of the internal manifold $T^{1,1}$. This construction requires turning on a worldvolume U(1) gauge field along the wrapped part of the D5-brane and dissolving some D3-branes in it. The stringy corrections play an important role in yielding a dS vacuum and the field strength of the U(1) gauge field must be sufficiently large to produce a tiny cosmological constant.

Overview of "De Sitter Vacuum on Nucleated D-branes with Stringy Corrections"

This paper presents a paper within the framework of string theory, elucidating the emergence of four-dimensional de Sitter (dS) vacuum solutions on D-branes nucleating in a ten-dimensional (10D) spacetime. Specifically, it examines configurations involving probe D3 and D5-branes that nucleate in an asymptotically $\text{AdS}_5 \times T^{1,1}$ background, with particular emphasis on the inclusion of stringy corrections. The author, Cao H. Nam, seeks to demonstrate how string theory, with appropriate modifications, can provide insights into cosmological observations.

Nucleation of D3-branes and the Role of Stringy Corrections

The nucleation of a D3-brane is investigated in a 10D bulk spacetime characterized by $\text{AdS}_5 \times T^{1,1}$ geometry, influenced by a sufficiently high chemical potential due to wrapped D3-brane charge. The paper reveals the existence of metastable dS vacua induced by stringy corrections, uplifted from the otherwise AdS state. The scalar field dynamics and the geometry of wrapped brane configurations are analyzed to extract meaningful cosmological implications. At zero order in the string length, it is found that no positive cosmological constant emerges on the D3-brane, necessitating higher-order corrections.

Analyzing the stringy corrections at the order $\alpha'^2$ leads to a positive cosmological constant on the worldvolume of the nucleated D3-brane, suggesting a mechanism through which observed tiny cosmological constants can be achieved. The findings indicate that the relation among the string length, AdS radius, and the observed Planck scale demands these α-corrections, providing a crucial improvement over models lacking these terms.

D5-brane Probes and Implications

Moving beyond the confined propagation of fields on the D3-brane, the paper explores the nucleation of a D5-brane, considering fields that could propagate in the extra dimensions, a promising approach for tackling cosmology and particle physics puzzles. The D5-brane wraps around a two-torus within the $T^{1,1}$ manifold, featuring a Chern-Simons term that includes a U(1) gauge field. The presence of dissolved D3-branes within the D5-brane structure is crucial for generating a repulsive force on the wrapped brane, attributed to stringy corrections and gauge field strength.

This construction underscores how stringy corrections and sufficient gauge field strength are pivotal to yielding a consistent 4D dS vacuum. The nucleated D5-brane expansion is scrutinized, and the emergence of a small positive cosmological constant is realized under specific configurations conditioned by large gauge field strengths on the brane, showcasing the flexibility and potential of the stringy framework.

Theoretical and Practical Implications

The paper advances theoretical understanding by showing how stringy corrections can naturally resolve the disparity between theoretical expectations and observed cosmological constants without necessitating precarious fine-tuning. It addresses scalar field inflation models within the string theory regime, contributing to the discourse on quantum gravity's intersection with low-energy effective field theories.

Practically, the paper speculates on mechanisms to achieve consistent cosmologies in higher-dimensional frameworks, informing both string phenomenology and landscape discussions. The dependence on parameters like the AdS radius and string length intertwined with the observable Planck scale provides key insights into bridging theory with experiment.

Future Prospects

The methodologies elaborated in this paper are pivotal for future explorations in string phenomenology, where understanding the vast landscape of possible vacua is critical. Investigating the conditions under which D-branes yield realistic effective field theories could spawn further empirical research in particle cosmology domains. Moreover, incorporating different compactification schemes and probing energetics of inflation further enriches the dialogue between theoretical predictions and astrophysical observations.

In conclusion, the exploration and modeling of D-brane nucleation processes with stringy corrections offer significant strides in reconciling string theory predictions with empirical realities, pushing forward the quest for a coherent intersection of quantum gravity, cosmology, and high-energy physics.