Freed-witten anomaly cancellation condition

Definition

The freed-witten anomaly cancellation condition is a criterion in string theory that ensures the consistent coupling of D-branes to background fields. It arises when considering the effects of D-branes in spacetime, particularly in relation to anomalies that may arise due to the presence of additional gauge fields or background fluxes. This condition is crucial for ensuring that the low-energy effective action derived from string theory respects gauge invariance and does not lead to inconsistencies in the theory.

5 Must Know Facts For Your Next Test

1. The freed-witten anomaly cancellation condition specifically applies when there are D-branes present in a background with non-trivial topology or fluxes.
2. This condition often requires specific conditions on the gauge groups and matter representations involved, influencing how D-branes can be configured.
3. It relates to the use of K-Theory to classify the D-brane charges, indicating how these charges interact with the background fields.
4. The cancellation condition ensures that physical quantities remain invariant under gauge transformations, maintaining consistency in the theoretical framework.
5. Failure to satisfy this condition can lead to anomalies that disrupt the stability of the low-energy effective action derived from string theory.

Review Questions

• How does the freed-witten anomaly cancellation condition relate to the stability of D-branes in string theory?
  • The freed-witten anomaly cancellation condition is essential for the stability of D-branes because it prevents anomalies that could arise from their coupling to background fields. When D-branes are placed in a non-trivial background, ensuring that this condition is met helps maintain gauge invariance and consistency within the theoretical framework. If anomalies were present, they could lead to inconsistencies in predictions made by the theory, thereby destabilizing the configuration of D-branes.
• Discuss the implications of violating the freed-witten anomaly cancellation condition on low-energy effective actions derived from string theory.
  • If the freed-witten anomaly cancellation condition is violated, it can result in physical quantities becoming dependent on gauge choices, leading to potential inconsistencies in low-energy effective actions. This violation could cause terms that should cancel out to remain present, which means that certain symmetries might be broken at lower energies. The resulting effective action could then fail to accurately describe physical phenomena, making it unreliable for predictions or calculations involving particle interactions and dynamics.
• Evaluate how K-Theory provides a framework for understanding the freed-witten anomaly cancellation condition and its relevance in string theory.
  • K-Theory offers a powerful mathematical language for classifying vector bundles associated with D-brane charges, thus providing insights into how these charges interact with background fields. By applying K-Theory, one can better understand when the freed-witten anomaly cancellation condition holds, as it directly relates to how these charges must align with the topological properties of spacetime. This evaluation shows that K-Theory not only helps identify configurations where anomalies can occur but also aids in constructing consistent models within string theory that honor the necessary conditions for anomaly cancellation.

Related terms

D-branes: D-branes are dynamic objects in string theory on which open strings can end, playing a significant role in the formulation of gauge theories and brane-world scenarios.

Anomaly: Anomaly refers to the breakdown of a symmetry in a quantum field theory, often leading to inconsistencies if not properly canceled or accounted for.

K-Theory:

K-Theory is a mathematical framework used to classify vector bundles over spaces, which plays a key role in understanding D-brane charges and anomalies in string theory.